I read there is something like 70,000 DHS armed employees not counting Border Patrol. So maybe 100,000 total, max? That would be 16,000 rds per employee or 4,000/yr. for 4 yr contract?
You're on the right track.
The contract was for 4-5 years, and the stated amount is an "UP TO" figure, not an actual ordered quantity.
In addition, DHS has training facilities that are available to all Federal LE agents of which there are somewhere around 150,000 and it appears that this buy is to cover all Federal LE issue & training ammo, not just the DHS proper.
Even if you figure that they actually do buy the entire 1.6 billion which is not at all a sure thing, it only works out to something like 2700-2100 rounds per Federal LEO. Not out of line at all, in my opinion.