The internal dimensions of Krag barrels vary greatly.  More of them measure .310 to .312 than .308.  But some are as small as .306.  Phil Sharpe wrote about it back in the 1930s and said he had tried to learn why and came up with no answer.

Ultimately, you will need to slug the bore and measure the slug accurately.  Shoot gas check bullets of at least groove diameter or a bit more, a good lube and do not try to set any velocity records. 

But undersized hard lead bullets will predictably leave lead deposits in the bore.  They will let the hot gas by and that will cause the leading.