[JAinSC]

I agree don't worry that much about depth. Even in clear water 10 feet is plenty for a warm weather flathead. With decent cover (floating dock overhead), just a few feet of water is plenty. Look for the biat. Where's the most food for those flatheads? Are there weed beds full of bluegills? Fish the fringes.

Also, don't be so sure they are not reproducing. If there's one male and one female, nature will find a way...

 

[JAinSC]

May have jumped ahead a bit - to target the flatheads, I would get good live biats (sunfish are always good) and fish with them after dark. Find an area that has good daytime cover (someplace for them to hide out during the day like a few good docks with decent depth - like 5 to 10 feet) and then an area nearby with good food - like weedbeds full of sunfish, or brushpiles sunk around the docks? Fish the deeper edge of the weedbed or fish near the brushpiles with the live baitfish from just before dusk until you catch a fish or can't stand it anymore.

Depth - Flatheads will hunt actively in as little as a couple of feet of water after dark if it's quiet. During day time they mostly settle into a secure spot that makes them feel safe, like a good stump or downed tree or under a dock, etc. If the cover is good enough they can be comfortable in a few feet of water, if there's no real good cover, they'll go deeper for security. You can coax them to eat during the day, but mostly they are just hanging out and waiting until it gets dark again.