It's all in 61.51-
§ 61.51 Pilot logbooks.
(a) Training time and aeronautical experience. Each person must document and record the following time in a manner acceptable to the Administrator:
(1) Training and aeronautical experience used to meet the requirements for a certificate, rating, or flight review of this part.
(2) The aeronautical experience required for meeting the recent flight experience requirements of this part.
(b) Logbook entries. For the purposes of meeting the requirements of paragraph (a) of this section, each person must enter the following information for each flight or lesson logged:
(1) General—
(i) Date.
(ii) Total flight time or lesson time.
(iii) Location where the aircraft departed and arrived, or for lessons in a flight simulator or flight training device, the location where the lesson occurred.
(iv) Type and identification of aircraft, flight simulator, or flight training device, as appropriate.
(v) The name of a safety pilot, if required by §91.109(b) of this chapter.
(2) Type of pilot experience or training—
(i) Solo.
(ii) Pilot in command.
(iii) Second in command.
(iv) Flight and ground training received from an authorized instructor.
(v) Training received in a flight simulator or flight training device from an authorized instructor.
(3) Conditions of flight—
(i) Day or night.
(ii) Actual instrument.
(iii) Simulated instrument conditions in flight, a flight simulator, or a flight training device.
So if your military paperwork has the when, where, what stuff listed above, it's good. As for the FR I'm guessing you're using some Air Force PC in lieu of the one hour ground, one hour flight. As long as you can explain what the paper says, that it gives you some flight privilege, you're covered. Expect some head scratching. I've only had one BFR in 34 years of flying. At the glider club I fly at, we get a yearly card saying we're up to date and good to fly. I find an airline pilot/CFIG to sign mine, explaining why I don't have a BFR to a pure glider CFI can take longer than the flight review would.