John, no, he doesn't have a military background, but he did start flying the P-51 at quite a young age. He, along with other airshow acts, certainly performs with military precision (as practiced over, and over again).
At one time I wasn't a fan of the aircraft, just going by the basis of the paint scheme that was dreamed up for it, but after listening to Scott's dad, Bill Yoak, describe the restoration and the meaning behind each individual aspect of the markings, I have since had a tremendous level of respect for Bill and Scott and the aircraft. Bill and Scott, father and son, restored the aircraft, and the aircraft was assembled from all NAA produced parts and skins, wherever possible, with very, very little of anything being newly manufactured, from numerous different sources. The metal work and craftsmanship on the aircraft is second to none.
There was a great film that I caught on one of the PBS channels about a year ago or so, that was filmed at Oshkosh 2007, that followed Bill and Scott Yoak bringing the aircraft to the show for the first time, and it also being the first time that Scott flew the aircraft during an air show display. (This was the same year that Gerry Beck lost his life in the landing accident in his P-51A, and this film included that, and it was quite remarkable seeing the effects of something like that on the fellow warbird and display pilots at the time, and their emotions and reflections as they continued to go about their business the next day, to go out and fly and display, after having lost such a close friend)