Flecto Varathane coloured enamel thinned slightly with some mineral spirits levels out and looks glass smooth. It would be an option for a brushing job that you want to look decent.

Also unlike a lot of spray cans it is likely going to be far more compatible with the existing paint and bond decently. But the key is to first prep the frame by using a wax and grease remover (from autobody paint suppliers) and then wet sand the existing finish to dull it and give some "tooth" for the enamel going on. Once this is done ONLY handle it with gloves as even your skin oils will affect the bond. You'll need to somehow feather in or fill out the existing chips and scratches. That part is up to you but I suggest leaving the Dremel alone. Use a slightly coarser grit wetordry sandpaper to feather in the chips and spot touch those areas with a little spray primer. Feather in with 600 to prep for the enamel.

The enamel stays tacky for a few hours so the trick is to work in an extremely dust free setting. How you achieve that is up to you. After the initial drying takes place overnight you can "bake" the paint to dry more fully and harden putting it in a small room with a heater. Or just wait for a week to 10 days before putting the bike back together.

I've found that the Varathane is tougher than Krylon and Tremclad or Rustoleum. Tremclad and Rustoleum are terrible paints BTW. VERY soft even after months. But it's not as tough as a proper factory finish or powder coat. But for a $30 10 speed at least you can keep the repainting costs down to about $20 and have lots left over for 5 or 6 more frames and forks.