can i make a free pokedex app?

Take the sprites [animated from a later gen such as 5 would be better] and all the information [from combined in game pokedexes and websites like bulbapedia or serebii] and just compile them together.

The easiest way to get the sprites would be to download a ROM of Black 2 or White 2 [as they contain sprites for ALL current pokemon] and run it through an editing program.

After you've got all the sprites and info, just compile it into a cohesive experience.

Just make sure to let people know [by including a small screen sequence or disclaimer] that even though you made it, Pokemon is still owned by Nintendo, Pokemon Company International, and Game Freak. Also have it state that you're not affiliated with them, and that this is 3rd party freeware.

[Gotta make it freeware, because if you try and charge for the pokedex app that you make; you're profiting off of other's copyrights, and they'll shut ya down for that. Even if you make the disclaimer about how none of what was used is yours.]