When I turn on my shower, the cold side has a steady strong flow. The hot side, however ; has a weak flow and makes that "hammer noise. If I flush the commode the hammering stops until the commode refills then it starts again. Ahy ideas?

I've heard a Plumber years ago say to correct this, if the dampers/air chambers are filled with water. Is Shut water off, open Faucet to let the water drain out, then turn water back on. Never needed to use this. Hope it works.
New house, or did this just start happening?

Water hammer is one loud bang when a fast acting valve shuts off. The sudden stopping of the water flow causes the pipes to bang against a structural member.
I am reading your "hammer noise" as a constant, rapid taping noise such as tap, tap, tap, tap while the water is flowing.
That would be caused by a loose washer in a valve some where. Most likely in the hot water side of the shower valve. Flushing the toilet changes the water pressure on the cold water side and the washer stops vibrating.

Remove hot water stem of shower valve and tighten washer.

Your right about the tap tap tap... I have a single handle to control hot and cold flow.. How would this change your diagnosis?

I tried turning off the main water supply , then opened all water the faucets in the house... kitchen , bath, outside ,flushed toilet.. in hopes of purging any trapped air.. No change... This is not a new house but . This is the second time this has happened in about 20 years and the first plumber had me to replace my water heater because pieces of the inside lining of the water heater had travelled though my water line and was was clogging my hot side faucet and causing the pulsating. Being a lot younger then , I took him at his word although I never saw the evidence. Being older and wiser ( and broker) , I want to fix whatever this is myself this time.

What the plumber was speaking of was a deteriorated dip tube in the water heater. Water heater have a plastic tube on the cold water input side that take the incoming cold water to the bottom of the tank. The hot comes out the top. Sometimes these tubes break up or crumble. This material can clog valves. Also when this happens the cold water will come in to the top and travel directly across to the hot water output.

The loose washer can be in some valve other than the tub. First try closing the stop valve under toilet tank about half way and see if that makes any difference. Next do the same thing to the cold water input stop valve on the water heater.

If these don't make any difference suggest you disassemble the shower valve and flush. Look for small particles of white or gray material.