hmm.. my memory didn't serve me well. Now that i have a muffler in front of me i see there is a heavy metal "ring" between the flare and the clamp. Sorry about that.. Clue me in as to what's actually broken or missing.
If that heavy metal ring that pushes against the flare is broken, a new one can be easily made on a lathe.. i can supply the dimensions if yours is gone. However, that ring must somehow be slipped over the tube.. and that will involve cutting the tube and welding it back together.
So, for what it's worth..
Assuming that your flared end is gone, and that ring is not damaged, i will tell you what i think about repairing the flare.
You can flare the tube's end again unless a lot of metal has rusted away... You can do it with a small hammer a flat punch and a vice to hold the pipe. First heat the end of the tube red hot and let it cool slowly to soften the steel.
It might take an hour to hammer a new lip on the tube. Taking care to not collapse the tube in the vise, make the bend around the circumfrence at 90 degrees. The flare's outer edge extends only 1/8 inch (3mm) from the tube. Afterwards, grind or file it's edge to a nice round shape of the right outer diameter.. (1-1/8 inch diameter) (This outer diameter will fit into the thick metal ring's depression)
Then lightly file the face of the new flare flat, so it can mate flat against the exhaust gasket.
An alternative would be to weld a steel washer of appropriate inner and outer diameter to the very end of the header. I think that a perfect silver-solder job (using genuine high-silver solder... melting temp around 1400F) would hold since i have used hard-solder close to the exhaust port without failures.. The header gets hot but not red hot...
Since the header will be slightly shorter using the above methods, slight bends to the header tube and/or re-drilling or enlarging the holes in the muffler's attachment tabs will likely be needed.
So, another alternative would be to make a short, perhaps one-half inch long, flared tube and slide that into the old header tube. This will allow perfect adjustment so that no bending of the tube or re-drilling of muffler attachment bracket holes will be needed. Weld or hard-solder the short tube once it's proper placement has been determined.