Pat fillets dry; slash skin side of each crosswise in 2-inch intervals. Season generously with salt and pepper. Sprinkle with flour to evenly coat, shaking off excess.
Heat oil in a large skillet over medium-high. When oil shimmers and wisps of smoke rise from skillet, add fish in a single layer, skin-sides down. Reduce heat to medium; cook, undisturbed, until skin is crisp and flesh is opaque halfway up sides and almost cooked through, 5 to 7 minutes, depending on thickness.
Flip and continue cooking until just cooked through, 1 to 2 minutes more.
Transfer to plates, skin-sides up.
Add vermouth to skillet; boil until mostly evaporated, 1 to 2 minutes.
Add capers and butter; cook until butter simmers and sauce thickens slightly, about 2 minutes.
Remove from heat; stir in herbs.
Return fish to skillet, skin-side up; spoon butter sauce over top. Serve immediately.
