Maggie, I'm pretty sure your boy has ich but I doubt he has velvet. Pata's right, lots of bettas have a golden sheen to them. The whitish stuff you see him shedding off is probably excess slime coat. When a fish has that many external parasites, he will create lots of slime coat to try and dislodge them. That slime coat will then shed off, creating the whitish blob stuff you're seeing.
The best way to treat ich is with AQ salt, high heat, and lots and lots of water changes. Here's how you can best go about it:
First, make sure his water is super clean and free of medicines. Get aquarium salt. You'll want to measure out 3 teaspoons of aquarium salt. Dissolve this salt in a small bowl of dechlorinated water (water treated with water conditioner). When it's dissolved, pour it into his tank. Now, if you can, turn up the heat in his tank to about 28 or 29 degrees celsius. He needs high heat because it speeds up the life cycle of the ich parasites.
Here's the important part. Every day, you need to remove your betta to a separate container and dump out all the water in his tank. Rinse it and refill it with dechlorinated water and the 3 tsps of AQ salt. Make sure the heat gets back up to 28 or 29 and then add your betta. This way, he won't get shocked by the temp. Do this every day until you don't see any white parasites on him. Then continue with the treatment for an additional 3 days. After that, you can stop and gradually readjust your betta to normal temperatures and remove the salt from the water.
The key is the water change because it removes all the parasites that have fallen off. If you don't change the water, the parasites will just reattach.
I hope this helps you, Maggie. Good luck and keep us posted. :)