Your challenge will be to find any 30-40 Krag ammo. Supposedly Hornady is going to start making it. If you do not reload, now would be a good time to consider that option. You can still find brass.

There are a few 30-40 Krag manufacturers out there but its really expensive.
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Remington and Hornady ammo are available.  Hornady started producing it last winter... and Remington has actually stepped up production for the first time in years.  Check Cabelas if you can - Remington ammo is usually available there.  Also, Grag and Sons has both Remington and Hornady ammo in stock.  As far as we know, all factory Krag ammo is manufactured to be within acceptable pressures.

Cabela’s website does not even currently list Remington 30-40 ammo and the Hornady is on backorder. The only place I have been able to find it for a while is at gun shows at scalper prices. Maybe that will change if Remington is putting some out. Hope so anyway. Never have seen modern FMJ 30-40 ammo.

No problem with FMJ bullets in a Krag.  Any .308 bullet will work as long as it's loaded within acceptable pressures (below 40,000 CUP).  That said, the Remington and Hornady ammo are generally good for hunting and accuracy is average.  Better accuracy is achieved with handloads and bullets that take advantage of that 30 inch barrel.  Just like humans, not all Krags like the same foods.  Some prefer the 220 gr RN loaded to original .30 Army specs... while others like 180 gr Spitzer bullets.  I have a friend who wins matches shooting a 150 gr RN bullet.  Also, not all Krags will feed spitzer bullets reliably - some hang up, some won't feed without problems.  If you do resort to handloads (like so many of us do), you just need to find what works best for you and your Krag!