welcome to the site,glad to have you! lots to learn here, make good use of the search functions as almost all the info on catfishing you could need is a click away on here. and don't be afraid to ask questions either, lots of good folks on here will help you out.
I fish what I consider to be a small to medium river. The deep holes are generally just over 10 feet. Even at night, I still fish just outside the cover on the deep side, at the head of holes, on points on the bank (a point on a river bank - where the bank juts out a bit on an otherwise fairly straight stretch - will usually have a bit of a washout hole off it from the current pushing around), the corners of sandbars, etc. I also get some good fish out on the flat toward the middle of the river sometimes, though.
Generally I am looking either to fish around good holding cover (I believe that even at night, flatheads spend a lot of time sitting in or near cover waiting for food to come to them) or some kind of a funnel spot. By a funnel, I mean something that will concentrate fish by sending them through a particular path if they are moving up or down river. This could be a spot where the river narrows or the narrows off a sandbar or a fairly narrow shute of deeper water when the rest of the river's width is real shallow or ... Just picture yourself as a fish trying to move up stream or down and figure, like a deer in the mountains or any other game animal, you don't want to have to go far up and down (deeper or shallower by much). Then where's the easiest route? Most animals also have a tendency to follow edges rather than wander in the wide open, right? Like the edge of a drop off or the edge of good woody cover, etc.