Toss sprouts with lime juice in a small bowl; season with salt and pepper.
Heat oil in a medium skillet over medium-high. When oil is hot, crack both eggs into skillet and season with salt and pepper. Oil should be bubbling around eggs from the start. Cook, rotating skillet occasionally, until whites are golden brown and crisp at the edges and set around the yolk (which should be runny), about 2 minutes.
Add red pepper flakes to oil and remove pan from heat. Meanwhile, heat tortillas over a gas burner until just warmed and slightly charred in spots (or warm in the oven or a toaster oven).
Mound sprouts on tortillas and top with fried eggs. Spoon chile oil from skillet around and drizzle with hot sauce. Crumble feta over, and serve with avocado slices, lime wedges, and more hot sauce.