Skates, move away?
Just a tip that works pretty often. Skates and fluke definitely dwell in the same areas. If you are having a skating party ( oh no, not another spinner!!). DON'T move to another area. Usually the skates will bite on the weaker portions of the tide, when it is hard to get good drifts.
When you find yourself getting too skatey, just tie your fluke rig leader anywhere from 12 to 18" above your sinker. Skates are always shoveling through the bottom and are often attracted to the bait by the smell. Fluke, being predatory, will look up and attack the swimming bait off the bottom if it looks good.
That is why, as Capt. Neil says, he usually catches his biggest fluke on the teaser. This works for almost all rigs, silver bullets, spin n' glows, skirts, rubber squids,etc.!