Such an app would basically just be an interface to a giant table listing pieces for every possible combination of moves. Assuming you could create that table, the app would be straightforward. I question its usefulness, though.
Firstly, most of the table would either be empty or taken up with obscure pieces that few would be interested in. For every combination of squares you could light up that corresponds to a common compound, there's a ton of combinations like "forward and left as a knight, forward and right as an alfil, or backwards as a ferz or rook" that are just weird. I'm sure you can dig up names and variants for several pieces like that, but it could take a lot of work if you're really being thorough, and the odds of a user stumbling upon any particular one of them are pretty low.
Secondly, for popular pieces, there would be an unwieldy amount of information to display. Take a look at the Piececlopedia page for the Bishop-Knight Compound, for example; it's got a bunch of different names and has been used in a ton of variants (the list on that page can't possibly be complete, but it's already more than one screen of info).
Thirdly, your database would have to leave out (or misrepresent) a lot of important and interesting pieces, because pieces aren't defined only by which squares they move to. The Knight, the Mao, and the Moa all move to the same squares, but they take different paths to get there. Some pieces, like the Cannon, require a hurdle to move. Some pieces capture differently than they move; Ultima is a variant based around giving every piece a different method of capture. Some pieces can make special moves under specific circumstances, like the pawn's initial double-step or en passant capture in FIDE. Some pieces just have weird special rules, like the ability to capture multiple times during their movement, or copy another piece's movements, or move other pieces with them.
Such an app would basically just be an interface to a giant table listing pieces for every possible combination of moves. Assuming you could create that table, the app would be straightforward. I question its usefulness, though.
Firstly, most of the table would either be empty or taken up with obscure pieces that few would be interested in. For every combination of squares you could light up that corresponds to a common compound, there's a ton of combinations like "forward and left as a knight, forward and right as an alfil, or backwards as a ferz or rook" that are just weird. I'm sure you can dig up names and variants for several pieces like that, but it could take a lot of work if you're really being thorough, and the odds of a user stumbling upon any particular one of them are pretty low.
Secondly, for popular pieces, there would be an unwieldy amount of information to display. Take a look at the Piececlopedia page for the Bishop-Knight Compound, for example; it's got a bunch of different names and has been used in a ton of variants (the list on that page can't possibly be complete, but it's already more than one screen of info).
Thirdly, your database would have to leave out (or misrepresent) a lot of important and interesting pieces, because pieces aren't defined only by which squares they move to. The Knight, the Mao, and the Moa all move to the same squares, but they take different paths to get there. Some pieces, like the Cannon, require a hurdle to move. Some pieces capture differently than they move; Ultima is a variant based around giving every piece a different method of capture. Some pieces can make special moves under specific circumstances, like the pawn's initial double-step or en passant capture in FIDE. Some pieces just have weird special rules, like the ability to capture multiple times during their movement, or copy another piece's movements, or move other pieces with them.