Can't book on a U.S. flag carrier? There's a form for that.
The Fly America Act is federal regulation that requires booking with a U.S. flag carrier for travel that is reimbursed from federal grants and funds regardless of ticket cost or convenience.
When it's not reasonable to fly on a U.S. flag carrier, there are excptions to the Fly America Act that must be documented on the Fly America Exceptions Form and attached with expense reimbursement request. Important to note that the exceptions provided by the Open Skies Agreements for government-funded travel do not apply if travel is funded by the Department of Defense (DOD).
See UVA Finance's website to learn more.