Clamps if it makes you feel better, but no screws.

If the duct is firmly secured to the joists, clamps arent necessary, foil tape should be sufficient. But if the duct support allows any movement, clamp them first and use tape over the joint.

Edit: Screws will collect dryer lint and eventually clog the duct producing a fire hazard.

From the Whirlpool Dryer Owners Manual > Home Venting Requirements: "Use clamps to seal all joints."

Sktn77a, why do you clamp before taping? The video I watched did it in reverse and none of the comments from pros mentioned that.

Would 2 layers of tape be better, one under the clamp and one over? I do not expect to be graceful with the tape while I am in the crawl space.

There should be no need for screw ("worm gear") clamps on the permanent duct. Those are for the transition duct to dryer and at wall, where you will need to remove the transition duct.

Using a brush on a drill will not dislodge the duct. Why? Because you need to use 28ga sheetmetal duct (code) which is fairly stiff, support min every 12' (duct comes in 5' lengths, so support at 10' seems logical), so will be very solid if installed correctly. Also you may not have a pest screen on any dryer termination cap (code). The best cap is a hooded cap with damper built in (damper also code).

"Sktn77a, why do you clamp before taping?"

I's not really a before/after thing. The clamp won't be right at the edge of the female end of the duct so you'll clamp it to make sure you lock in the male end, then tape over the edge of the female end. You could certainly tape first and then clamp over both (over the overlap).