Flatten one side on a disk sander. Make one for your lathe; it's pretty easy to make a 12" disk sander that way. Or, use a flat plate and a sheet of sandpaper. Anyway, get one side of each ring flat this way.
Now, what I do is glue the rings on one at a time. Each ring is trued on the lathe after gluing. I usually keep the piece on the lathe for a day or two at this point; the tailstock holds the ring in place while it dries, then I true it, then the next ring, etc.
To true the ring flat, first use a scraper or gouge to mostly flatten it. Check regularly with a straightedge long enough to span the diameter of the ring. When it's close, switch to a long block of wood (again, long enough to span the ring) with sandpaper wrapped around one end (for small rings, use sandpaper big enough to span the rings also). You should be able to get a light-tight fit this way.
To minimize glue lines, what I do is this: I have a flat board with a small hole in the middle and four blocks bolted on via slots. I use the blocks to align the ring and keep it centered on the hole. The hole is where the tailstock goes as the ring is pressed against the rest of the piece. I apply a little pressure, then start turning the ring relative to the rest; this motion helps the excess glue squeeze out. I tighten the tailstock as the glue is squeezed out, until the glue layer is thin enough resist turning. I think the friction and thin layer helps it set faster; I can usually turn after only an hour this way.