Gee, I have no idea what the background is of most of the thriller writers whose work I enjoy. I always assume they're kick-ass researchers.
I liked Vertical Run by Joseph Garber, in which a businessman uses skills he hasn't employed since 'nam. No idea if Garber was there, though.
Here's a short list of thrillers I've enjoyed enough to recommend them to others.
Peter Abrahams, Pressure Drop, The Fan, Hard Rain, and Revolution Number 9
Lawrence Block, A Long Line of Dead Men (just one of a large series)
Harlan Coben, Gone for Good and Tell No One
Douglas Kennedy, The Big Picture and The Job
Andrew Klaven, True Crime
Dennis Lehane, Mystic River and Gone, Baby, Gone
Elmore Leonard, Get Shorty, Rum Punch
Michael Malone, Uncivil Seasons
T. Jefferson Parker, Silent Joe
Petru Popescu, Almost Adam
Stephen White, Kill Me
I know a little bit about some of those authors, and my understanding is that their careers as newspapermen, attorneys, psychologists, whatever influenced and informed their novels far more than military or police work. I'm not sure any of them were policemen, although several are of the age when they could easily have been drafted to serve in the military if they did not volunteer.
If the thrillers you like most involve law enforement or military matters, then you will need to do research and make some connections with people you can ask if you're not sure you got something right.
Maryn, who loves her some thrillers