I wasn't clear, but I was referring to radial slop, not rotational slop (there should be a little of that from the gears that drive it). If the shaft wobbles in the body of the distributor, I wonder if this could be the problem: the slop in the distributor shaft doesn't allow the spark to get from the rotor to the cap electrodes reliably as well as some interference between the rotor and cap is causing the flaking. I'm thinking the fact that you're having trouble with #2 and #3 (did I understand that correctly?) might also be evidence of that. Otherwise, I would think the same cylinder would misfire - in which case I would change that plug and try again. The thing that makes me wonder is that I would expect that you'd see evidence of arcing from the rotor to the cap.
I have to say, the only problem I've had with a distributor is when the one on my Ford Probe went out and left me stranded, so I don't have a lot of experience to draw from. I guess I've been lucky. It might be time to find a shop with an old distributor machine (if there are any more) and have it tested or inspected to possibly rebuild it.
A couple of things come to mind when thinking about this. First, if you don't have one all ready, I would advise getting and installing a Pertronix ignition while the distributor is out. Second, you do know that you folks who have Twin Cams actually have Triplet Cams?