Ding...here I am chiming in. Let me add my experience also includes two years enlisted in Army air traffic control and 500 hours in the Huey as a Warrant Officer Aviator in the Guard in early 1980's. The ATC experience went over well in the interview. I also had an interim job flying ISR in Iraq after I retired from active duty which got me the required recency of experience (100 hours in the last 12 months) to qualify for the FAA job. Dual ATP RW/FW.
FWIW - I had ~1000 hours in the U-2 which is counted in my tail wheel time; not that it matters at all for this job other than the fact that they like to see that you are truly interested in all aspects of aviation and are ready to spend a lot of time on the road followed by the appropriate time and attention to detail in the office completing the required reports on the facilities checked. USMC Flyer can elaborate on what the job really entails as I just hired on.
The interview was straight out of the pages in this thread. Very straight forward. Nice folks.
The best advice I can give for getting this job is to drop in on one of the offices, meet the guys and see the operation. Talk to the crews if you meet them on the road. Realize you will have to move to one of the Flight Check office locations (on your own dime) and plan to be there for two-three years or more. This is not a commuting job and you are in the office/on the clock when you are not on a trip. It takes several months to get a new pilot up to speed and no one wants to see them try to transfer out as soon as they are qualified.
That's my 2 cents as a FNG who has not even gone to the sim yet. USMC can tighten me up as required.
HH