1. So, what is this type all about?
This type is proposed generally as a means of separating bird-related moves from Flying-type, much like how Wind-type is generally discussed.
The primary difference between the Wind-type and this type is that most RPGs who have a Bird-type generally use it for avian species such as SMT's Flight, with the possible exception of Digimon, which uses Bird-type for Bird Digimon, but in that case Bird-type is just species classification. So, for most part Flying covers general RPG usage of Bird-type.
2.Where does this name come from?
The name comes from a glitch type in Gen I and Gen II games, which generally thought to be the predecessor of Flying-type.
3. Does this type have an in-game source?
Yes. In addition to above, we have several Bird-related moves such as Sky Attack(Jp. name: God Bird) and Brave Bird, as well as some bird related abilities such as Big Pecks and Tangled Feet.
In addition, there is a dedicated Trainer Class for Bird Pokémon, the Bird Keeper. Falkner is also based off this concept
4. What would be the ideas behind such a type?
Most obvious idea behind this type would be the wide majority of flightless birds.
Most obviously, this type would be primarily about extinct flightless birds.
5. What would be the type interactions of such a type?
Basically it would be the current Flying-type without Ground immunity and Ice weakness.
6. What would be the distribution of such a type?
Pure variants would be rare, due to non-presence of flightless birds in the real world due to recent extinctions.
But common variants would be common, as Bird Pokémon are early route Pokémon.
7. Future comments:
The primary issue behind this type is that it would have to be seperated from Flying-type and Normal-type, causing them to lose a lot of decent moves, abilities, and so on.
However, because bird-based Pokémon are so common, having a dedicated bird-type, even for flightless birds is simply unnecessary in the current scheme of things.