Yes, you can catch speckled trout on a fly rod, and when you get into a school, the action can be “a fish on every cast” frantic.
The best setup is a 6-weight fly rod loaded with a 250-grain, integrated shooting head line like Orvis’s Depth Charge. Attach a 6-foot length of heavy leader (50-pound monofilament) and 18 inches of 20-pound fluorocarbon leader. A good fly is a colorful, 3-inch Clouser in pink, yellow, white, chartreuse or a combination. This setup will get the fly into the strike zone, which is about two feet deep, with a moderate speed retrieve.
Cast into the shallows and retrieve with and across the current. Unlike the strip-strike hookset used with redfish, a sweep hookset like freshwater trout fishermen use works well.
Good spots for this technique target trout working baitfish against oyster banks.