Is there anything that would prohibit us from purchasing direct from the Air Force Program Office if they are able to accept and use our funding?
No, there is nothing in the FAR or DFARS that would prohibit this transfer. You might have some internal organizational procedures that you need to check.
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Transfers between military departments are called "assignments" and addressed in DFAR 208.7002, Assignment Authority. Paragraph 208.7002 (a) (4) (i) says the "submission of a military interdepartmental purchase request (MIPR) by a requiring activity and its acceptance by the contracting officer of another department...constitutes a one time agreement."
Your issue is within a military department, and the transfer should also be executed by a simple MIPR of funds from your organization to the organization providing you the item. Once again, this type of interdepartmental transfer is not addressed within the FAR or DFARS.