>>48266220Everdrives, reproductions and flash carts alike can't transfer up to the next generation. You can still trade to a real copy to transfer up though, as the hardware is just running the ROM like a real GBA game once the game is loaded. The problem with flash carts, repros and everdrives is that the DS can't find the right memory locations when migrating.
Ironically, having a real GBA game and migrating to a fake gen 4 game or flash card works, since the DS is able to treat the loaded ROM in the flash card/fake just like any official game on the hardware. Similarly fake gen 4 to real gen 5 doesn't work, but real gen 4 to fake gen 5 works. Fake gen 5 to bank doesn't work.
What you could do besides trading to a real gen 3 game is transfer the Pokemon from your gen 3 flash cart save to PKHex and just migrate them up by hand to a DS save on a flash cart. Trading between fake and real games of the same generation works for gen 3, 4 and 5.
Gen 1 and 2 fakes and reals are all able to interact with one another including GBC flash carts, though not from a GBA Everdrive/flash cart. The GBA flash carts can run GB/C games though emulation, not the official Gameboy hardware part of the GBA.