Tabitha,
We are pretty big seafood fans, and Flying Fish is one of our favorites. But like you, we can only fit in so many signature dining experiences into our vacation plans.
Of the seafood-centric alternatives out there, here are a few suggestions;
Coral Reef Restaurant (Epcot): Located inside the Living Seas Pavilion, this is a good alternative for a few reasons. It is just a walk away from the Flying Fish, so if you are planning meals based on where you will be on specific days, it helps. It also has decent seafood. The view into the pavilion aquarium is great, even if the room is a bit cold inside.
Kona Cafe (Polynesian Resort): While the menu is not seafood exclusively, it has several good choices, as well as an adjacent sushi bar. The setting in the resort is also nice, if a bit noisy.
There are others, but these are my two top suggestions. Either would do well, though I think for a purely seafood dining experience you might prefer the Coral Reef.
Write me back if you need any other dining suggestions.
Have a magical (and delicious) vacation!