They're never called Flickies in the game, or any of the Japanese guide books, or Gamma's profile on Sonic Channel. (Or even in Sonic X, which does name-drop Flicky in reference to the original version.)
Their design doesn't match up with the original Flicky or any of the Sonic 3D Flickies either.
Calling Sonic Adventure's bird trio "Flickies" was always just a fan assumption thing. But Sonic Adventure's penguin isn't a Pecky, the seal isn't a Rocky, the rabbit isn't a Pocky. There's nothing to suggest that the birds should be thought of any differently.
I also agreed with Pengi - Amy Rose called the bird that crashed into her "Bird" or "Birdy", but never "Flicky" as far as I know. Same thing go for Eggman, he yelled "get that bird" before sent E-102 to grab it from Amy Rose while she was in the prison, only to have E-102 freed them instead.
So make that those animals appearing in Sonic Adventure more "normal animals" than the ones coming from Sonic's world.