Okay so I have an old road bike with 650A wheels and 120mm spacing on the rear forks. I don't know much about wheel sizes or even how to shop for them. I want to put a wheel with a flip flop hub on the back of my bike. I doubt I'll find something like that in 650A.
I assume I'm right in thinking I could put some 650B wheels on this thing because B is smaller and they only differ by 6mm.
1) Am I right in thinking I'm only going to need to adjust my brakes down about 3mm?
2) Where can I find a 650B (A is fine too, on the long shot) rear wheel with a flip flop hub? For cheap?

Edit: I didn't even think of 700Cs. I have about an inch of clearance from the tire that's on my 650As. Not enough? Certainly the brakes won't fit, but would the wheel?

It sounds like a custom wheelbuild situation.

What you are asking for is not commonly available, and therefore not cheap.

bummer.

650B doesn't come much more ready-made either, but the wheels are no harder to build yourself than any other size wheel. The 3mm radial difference should be easy to accommodate with most brake calipers.

650B is making a comeback. QBP is stocking some wheels and tires.

Sun CR-18 rims in 650a are good. Lace 'em to a 120mm hub (Phil Wood track flip-flop if you want to get crazy) with butted spokes and build 'em up yourself. It's hard but a good learning experience and is well enough documented that you'll likely see success on your first try.