Just a dumb question: How are you going to fit your barrel blank to anything, if you don't have a lathe?
Chambering the barrel is about the last thing you do.
You still need to profile a blank to give it the shape you want, or, if you're really lucky or very accepting and it has an acceptable shape, you'll still need to crown the muzzle and fit the thing to your firearm ... either threading or some other work. And last, once everything else is known, you'll chamber, with the appropriate head space. Somewhere in there, an extractor cut, and maybe some work on a "ramp"... unless you're building a zip gun.
Can you do all this with an old hand file while squatting cross-legged in the dirt, which is basically the future of machining anyway in NDP Alberta?
Sure.
Do you want to do it this way? I know I don't. With a lathe, milling machine, a handful of other power tools, a TON of bits and cutters and reamers in my shop ... I'm still feeling under equipped.
Just for fun, I did recently buy a 5.7mm carbide reamer from China for $17 (US, shipped, right from Hong Kong). That is the nominal size you need for a .22 chamber. I'll let you know when I find a bit of time to try it out. It could be used with a bit and brace or a power drill and some care, and you have to (OK: should) set a depth-stop. But the little 5-flute gem does look (and measure) pretty well. As a real test, I gently slipped it into a nice chamber I cut with a commercially made .22 chamber reamer and turned it backwards ... a perfect fit, as far as I can tell.
Should everyone rush onto ebay and buy these things, 'cause they're so much cheaper than a $40 proper HSS reamer? Probably not.
As for it being "Carbide", the Chinese reamers are labeled HRC40. I'm not sure what hardness good HSS cutters are, or what my commercial HSS reamers are, but some of my cheap cutters test at HRC60. The HRC40-labeled reamer is hard enough to make a dull spot on a no-name shop file though. We'll see how it does...
