How did "Good Kill" get the cooperation of the Air Force?

The 'Air Force base' was a regular civilian airfield dressed both practically and later digitally as an AFB. The drone footage is actually very easy to do in CGI. In fact the comparatively 'crappy quality' of real drone footage and speed of explosive shockwaves/debris-fields really help when creating CGI simulations as we don't expect realistic (and thus harder to create) views of this kind of footage. There's a first-person-shooter game called 'Arma III' that's like $50 and is so realistic, especially in it's use of night and heat-vision, that footage from the game pops up in all sorts of low-budget TV (think Sci-Fi channel). I suspect that the effects in the film were a combination of real footage from one of those $3000 quadcopters with overlaid CGI and the odd bit of practical dressing.

On a separate note I personally wouldn't say the film was too preachy, but I do know where you're coming from. The issue is that it's very hard to make a war/military film that everyone considers the same as everyone comes at it from their own perspective. For instance much of the world see's the last 15 years of US/UK (I'm a Brit btw) military intervention around the world as terrorism, so if you make a film focussing on the methods of that intervention then you're going to see if from either 'inside the machine' or outside - almost nobody will see if from a balanced perspective unless you really break things down analytically. Clint Eastwood is very smart guy and while his films and editing are notoriously simple affairs his understanding of balance in his war films is second-to-none. In particular "American Sniper" was seen by some as being very pro-US, others as being very anti and yet if you re-watch the film it's actually sitting on the fence quite nicely, not many can do that.