So, what is the Flying-type?
All JRPGs have some sort of Wind-based magic. Even in SMT, where Wind is called "Force", has Wind. This is present in most RPGs because Air is one of the prime elements in Greek alchemy. However, Flying is not based on the element of the Wind. Instead, it is based off Avian enemies that occur in most RPGs that are immune to Earth elemental. The concept of "wind" is not initially used by Flying-type, but rather Normal-type, with moves like Whirlwind and Gust, the latter of which originally was a Normal-type move. Why was this? Well, see the previous statement. But you might wonder, if Flying doesn't represent an element, but rather a class, what was Flying initially? Well, to answer that, we have to go before the Flying-type.
The Prehistory of Flying-type: Bird-type:
In the original development of the game it is hypothesized, but not confirmed, that there was no Flying-type, but rather Bird-type, an odd Glitch type that occurs in various glitch monsters in the first Generation. This is further emphasized by the fact that both Glitch Pokémon that get this type learn Fly and Sky Attack, the latter of which has the Japanese name of "God Bird". In fact, in Gen I MissingNo. is the only other Pokémon to get Sky Attack through Level-Up besides Moltres.
This idea is further evidenced by the fact that vast majority of Flying-type moves in Gen I besides Fly are related to Birds in their Japanese names, and the only non-Bird Flying Pokémon are Charizard, which is a Dragon, Zubat-line which belong to Flying Egg Group, insects, Gyarados who is also a Dragon and Aerodactyl, which is also closely associated with Dragons.
It is quite possible that all of Lance's team would have been Dragon-type if Bird-type wasn't scrapped in favour of Flying.
The History of Flying-type in Pokémon:
Now that's out of the way, let's discuss Flying. In the first generation, Flying was bad. It had no Gym, no E4 member(except Lance, huehue) and no dedicated support. It was a type that was meant explicitly to support other types, rather than be its own thing. Ice also suffered from this, but recovered from it recently. Flying however never truly recovered from it. The few major Pokémon that got the type got it either as a classification or as a nerf, in the case of Gyarados.
The strongest moves for Flying were Fly, a semi-optional HM, and Sky Attack, a TM that served as Moltres' pseudo-signature move. The Fly HM was originally exclusive to Flying-types, which made Flying Pokémon a necessity for all in-game teams, hence why Flying was introduced as a primary type.
Special split didn't affect Flying-type much. It just nerfed Gyarados and the Legendary Birds. Everything else either got the same Special in both of their stats, or in Scyther's case, got better Special in some other stat. This wasn't necessarily a buff, as besides the above mentioned four and Charizard, the only Flying-types with a decent special were Pidgeot and Butterfree. The newly introduced Flying-type Pokémon were largely gimmick monsters, special rare monsters with terrible stats but unique characteristics. Almost all of the Flying-types that were introduced in this generation had to be buffed significantly in later generations, except Crobat. Even Will's signature Xatu had to be given a powerful, rare Ability.
However, two significant moves were introduced. One was the retcon of Gust into a Flying-type move. The other was Aeroblast, a move introduced to Lugia due to fact that it wasn't a Water-type, and thus couldn't get a proper counterpart to Ho-Oh's Sacred Fire. These two buffs, though small, started the change of Flying-type from the "Avian" type to "Wind" type. Nonetheless, Flying remained as the "Avian" type in this generation, and its Egg Group, Flying, continued this idea, including most of all avian Pokémon, but not bird Pokémon themselves.
Third generation was another lost generation for Flying-type. While another wind based move was introduced, Air Cutter, the rest were largely useless, though commonly distributed. Gen 3 have helped Flying to become more of a conventional type than a classification, but that doesn't mean this generation made it good. The vast majority of the Flying-types introduced were just as gimmicky as the previous generation, despite most belonging to proper evolutionary families, and had to be rebuffed extensively, Ninjask and Tropius are the only ones which have not.
However, this generation also gave us the personification of the Flying-type, Rayquaza, and its Sky Tower. The latter would serve as a basis for later Dragon areas like Dragonspiral Tower, and the former would have access to Dragon-type as a reference to Twister, a Dragon-type wind-based move that would later be made available to Flying-types. This generation would also introduce Silver Wind, a Bug-type Ancient Power clone that is also Wind-based, and accessible to Flying-types.
Fourth generation would be less of a miss for Flying-types. Partially this was due to the fact that Gen 2 Flying-types gained new evolutionary members for their families. Partially this was because of Arceus, the first Pure Flying-type Pokémon. Partially this was because of Staraptor, a truly competitive level early game Flying-type. Partially this was because of Drifloon-line and Chatot, two Flying-type species introduced for primarily for marketing purposes. However, the biggest shock to the system was Physical-Special split. This made previously wind based moves Special, effectively making "Wind"-type the Special part of Flying-type. Several other great moves like Tailwind, Roost and Brave Bird were also introduced, making Flying fully developed as a type.
This generation also introduced Tangled Feet, an Ability associated with the type due to its Japanese name. However, in terms of the Ability front Flying-types didn't get much else. This generation also introduced several other wind-based moves like Heat Wave, Ominous Wind and Twister as tutors for Flying-types, but only Heat Wave remained.
Fifth generation was possibly Flying-types true rebirth.Three major competitive moves, Acrobatics, Sky Drop and Hurricane were introduced, with perfect timing. Acrobatics became a true threat due to Flying Gem, Hurricane became horrendous due to permanent Rain and Sky Drop had no weight limit. All three moves were nerfed in the later generations, crippling Flying-type for good. This generation also introduced the Kami trio, the most infamous legendaries in the game in terms of competitive play.
The conventional Flying-types introduced were not too powerful however. Emolga was the strongest Pikaclone, but that didn't mean much besides Elesa battle. Sigilyph was quite powerful, but due to its low stat total it could be get around. Rufflet-line and Mandibuzz-line were neat attempts at competitively viable late-game Flying-types with mixed success. Ducklett was introduced exclusively for a encounter gimmick and a group of new items for EV training, Wings. Woobat was just a weaker Zubat clone.
One more major introduction was Big Pecks, a new ability for Flying-types that was not too powerful but a clever pun both in English and Japanese.
Sixth generation was a very mixed bag for Flying-types. While Hawlucha was quite powerful and Talonflame was overpowered due to its Hidden Ability, the rest of the Flying-types were just improvements on previous others, Vivillon for Butterfree and Noivern for Crobat and Altaria. Several Mega Evolving Pokémon also lost their Flying-type for a better non-elemental type, like Dragon and Fairy. Nonetheless, with the new Aerilate ability, two megas, Mega Salamence and Mega Pinsir, made a splash.
In terms of moves and Abilities, Flying-type didn't gain much besides Aerilate. The rest were exclusive stuff for Legendaries, though Mega Rayquaza takes a special place due to being the strongest Pokémon in the game.
Seventh generation was another miss for Flying-type. With the Gale Wings nerf, the strongest early bird was no longer the stuff epic myth, but of rumor. The only new move introduced was a signature move to a early Flying-type that already got Brave Bird. The rest of the Flying-types besides Celesteela were purely gimmick. Nonetheless, some of the previously exclusive type combination were utilized in this generation and Flying finally rose to E4 status.
The Overview of Flying-types:
Flying-type was supposed to suck, but it succeeded by not sucking.
That is all there is to it, really. Flying-type was supposed to be another filler type like Bug, Normal and first generation Dragon that served as a classification rather than an element. But due to lack of a proper Wind-type, and the early push Flying-type as a nerf for strong Pokémon, Flying-type broke its chains, and became a powerful-type while remaining the third most abundant type, after Normal.
This was partially due to its abundance, which made Flying capable of interacting with other types, evidenced by moves like Ominous Wind, Heat Wave, Silver Wind, Icy Wind, Twister and to some extent Sandstorm. All of these gave Flying-type a connection with types other than itself. Flying-type also gained some moves from other types for itself, like Steel Wing, a move created out of Skarmory's type, and Flying Press, a move that emulates Hawlucha's type.
While these are all nice and dandy, it is important to remember that Flying the type and Flying Egg Group are still quite dry in terms of stats and moves due to their role as early route fodder, and as fodder for later sections of the game as well, due the Flying's origins as more of a category than an element.