Fearow's PokePower reads like this:
"PokePower: Delta Sign
Once during your turn (before your attack), you may search your deck for a Pokemon that has [Delta Species Symbol] on its card, show it to your opponent, and put it into your hand. Shuffle your deck afterward. You can't use more than one Delta Sign PokePower each turn. This power can't be used if Fearow is affected by a special condition."
If a card has a text in the PokePower like the one in bold print above, then you can only use that PokePower once during your turn. So if you have 2 Fearows out, you can only use one Delta Sign PokePower from one of them that turn, no matter what.
ANY card that says "Once during your turn..." on it, that just means for that specific Pokemon. For example, Flygon's Delta Supply PokePower states that "Once during your turn..." you may use that power. That's only for that Pokemon, since that Power is only an effect from that Pokemon.
Fearows PokePower, on the other hand, says that you can't use its Delta Sign multiple times, and using that specific PokePower makes it work that way.