.30-40 Krag and .303 British are dimensionally very similar.
What makes you certain it's a .30-40 Krag? Is the barrel marked as such? The military Ross rifles were issued in .303 British, and have a bore diameter a smidgen larger than the .308" of the .30-40 Krag. .303 British bores run about .310-.312", so a quick test is to see how a .308" bullet inserts from the muzzle end of that unloaded Ross rifle.
Your safest bet would be to have a chamber casting done, which would eliminate all guessing.
Perhaps somebody rechambered a Ross to the .30-40 Krag, but that would still be a sloppy bullet fit to the bore, unless it's a wildcat .31-40 Krag, just like folks did with their rechambered .31-06 Arisaka Type 99 rifles.