In a small bowl, combine the pineapple and lime juices and the salsa and set aside. Dry the fish fillets thoroughly with paper towels.
Spray a small nonstick skillet with vegetable oil cooking spray and put the pan over high heat. Dredge the fish fillets with flour, shaking off the excess, and sauté the fillets on one side until they are lightly browned (2 to 3 minutes).
Don’t move the fish around while it is browning or it will stick. Using two spatulas, gently turn the fillets over and brown for 2 minutes on the other side. Remove the pan from the heat and allow it to cool off a little before continuing.
Stir up the pineapple-lime salsa and pour it over the fish. Lower the heat to medium low and cook for 4 to 5 minutes, basting with the sauce once in awhile, until the fish is cooked through and the sauce has been reduced to a thick glaze.
Garnish with a sprinkling of green onions and serve.