Barrels, if in good condition, should be capable of dealing with more stout loads, but how stout? The Flues action was not designed for later 3” ammo, with higher pressures and greater velocity. That would be the NID job. It’s the velocity that might be the problem. The wood is 100 plus years old. Period 3” ammo included extra wadding for better patterns. Todays hyper velocity ammo should never be shot in it.

If you reload there are a number of options from Alliant, assuming you can find any, or Hodgdon web site. Blue dot for Alliant would be my first choice, ImR Blue or Longshot from Hodgdon. The Bluedot ends up about 1200 fps at 8,000 psi which should be fine. The modern 1300-1400 hyper loads, with chamber pressures in the 11,000 psi range are not anything I’d want to shoot in it. But your gun, your decision as they say.