Make the pico de gallo: In a medium bowl, toss together all the ingredients.
Fish
Prepare the fish: Mix the flour and seasonings on a plate. Dip the fish chunks into the flour to coat on all sides. Transfer to a clean plate.
In a large sauté pan, melt the butter over medium heat. Add the fish and cook until the fish is golden brown on the bottom, 3 to 4 minutes (depending on the thickness of the fish). Flip and cook until it is golden brown on the other side and the center is white, flaky and cooked all the way through, 7 to 8 minutes total (depending on the thickness). Add more butter to the pan if necessary to keep it from drying out. Squeeze the lime on top.
Serve the fish with warm tortillas and freshly made pico de gallo.
Notes
For spicier version, use a whole serrano or jalapeño pepper, or both!