#13: I already have an FAA Flight Instructor Certificate, but it has expired. Can I reinstate it with the new 14 CFR 61.73 military competency to Flight Instructor process?

No, you can't. Sorry. You fall entirely under 14 CFR 61.199 for the reinstatement of your certificate (and 61.199 was not re-written when 61.73 was). So although if you'd never have had a previous flight instructor certificate, you could just simply take the MCI test and get one, that doesn't work for reinstatements. Instead, since you do have a previous flight instructor certificate, you have to reinstate it by taking a checkride with a designated pilot examiner. Here are two examples:

Case 1. you hold an expired flight instructor certificate with room to add more ratings from military competency:

Let's say you have an expired Flight Instructor certificate with both Airplane Single Engine and Instrument Airplane on it (but you don't have Airplane Multiengine on it). Lets also assume you've been an IP in a military multiengine displaced thrust airplane like a C-130 or a P-3 or a C-12 (not a centerline thrust airplane... that's a different question). You have to take a checkride to reinstate your flight instructor certificate first. After that, you can turn in the paperwork showing that you are or were an IP in the C-130, and they will add Airplane Multiengine to your flight instructor certificate with no further testing of any kind.

Case 2. you hold an expired certificate with nothing to add from military competency:

Let's say you have an expired Flight Instructor certificate with Airplane Single Engine, Airplane Multiengine, and Instrument Airplane on it. Let’s also assume you've been an IP in a military single engine airplane (T-34, T-41, T-6, F-16, etc.). You cannot reinstate your certificate using 14 CFR 61.73 (military competency to instructor). You have to take a checkride to reinstate your flight instructor certificate.

We have included 14 CFR 61.199 below for your reference:

14 CFR 61.199: Reinstatement requirements of an expired flight instructor certificate.

(a) Flight instructor certificates. The holder of an expired flight instructor certificate who has not complied with the flight instructor renewal requirements of §61.197 may reinstate that flight instructor certificate and ratings by filing a completed and signed application with the FAA and satisfactorily completing one of the following reinstatement requirements:

(1) A flight instructor certification practical test, as prescribed by §61.183(h), for one of the ratings held on the expired flight instructor certificate.

(2) A flight instructor certification practical test for an additional rating.

(b) Flight instructor ratings. (1) A flight instructor rating or a limited flight instructor rating on a pilot certificate is no longer valid and may not be exchanged for a similar rating or a flight instructor certificate.

(2) The holder of a flight instructor rating or a limited flight instructor rating on a pilot certificate may be issued a flight instructor certificate with the current ratings, but only if the person passes the required knowledge and practical test prescribed in this subpart for the issuance of the current flight instructor certificate and rating.