Would it have no type? Or will it keep it's Flying type in this case?
It would become ??? type, or it would become normal type, depending on which generation.
If a Pokémon that has become a pure Flying-type uses Roost, it will become a ???-type Pokémon until the end of the turn.
If a pure Flying-type Pokémon uses Roost, it will become Normal-type until the end of the turn.
-Bulbapedia, Roost
Source