This is interesting:
The Air Force and coalition partners in the air war against the Islamic State are not only sharing intelligence, runways and strategic plans, they’re also sharing bombs.
Coalition jets having been taking from the U.S. stockpiles as needed, said Lt. Gen. John Raymond, deputy chief of staff for operations at Headquarters Air Force.
We tend not to encourage allies to have large stocks of ammunition for US-designed weapons because we don't want allies to have the ability to wage a war for long that we disapprove of.
So allies who are bombing in Syria and Iraq grow short of ammunition. And we supply them with our far larger war reserve stocks.
As we've done for allies bombing Yemen. And as we did for allies bombing Libya.
One interesting stockpile of ammunition we maintain is in Israel. Technically, it is meant to be for our use, but I fail to see how a stockpile in Israel is more useful than a stockpile more convenient to the Persian Gulf region.
This seems like a way to provide Israel with ammunition resupply quickly (recall the major--and inconveniently high profile--effort by air in 1973) if we approve of the war yet prevent Israel from controlling the ammunition if they fight a war we really don't want to support.
It's tricky. Before 1965, Pakistan only pretended to use up ammunition we provided for training in order to build up a war reserve stock to attack India.
So we can't fully guarantee that allies will only fight for objectives that we want.
We do know, however, that we have no real problem with allies bombing targets in Iraq, Syria, and Yemen. That's why they are resupplied from our stockpiles.