Mix the coriander, paprika, and garlic powder in a small mixing bowl.
Pat the trout fillet dry. Sprinkle with salt and black pepper on both sides, then season with the spices on both sides.
Coat the seasoned fish with the flour, shake off any excess flour (you only want a very thin layer).
In a large cast-iron skillet, heat about 3 to 4 tbsp olive oil over medium-high heat until shimmering but not smoking (see note). Sear the trout fillets for 3 minutes on each side (start with the skin-side down, and use a spatula to very carefully flip the fish fillets over).
Remove the fish from the pan and place it on a tray lined with paper towel to absorb any excess oil.
Transfer to serving platter and finish with a squeeze of fresh lime juice.