Was your uncle military? Traditional military garments, that is, garments made to fulfill a specific contract and issued to military personnel as part of standard issue kit, are devoid of brand tags. They state only the description, or line title, of the item, size, material, and care instruction. They don't allow branding of the item IF the item is prepared for a military contract. Issue bomber jackets often have velcro (loop side) patches on the chest for name badges and unit patches, since the pilots/crew often changed squads or commands. The "TES" insignia, in current acronym standards, would be a Test and Evaluation Squadron, so for an actual flyer this would be a test squad for modified aircraft or to qualify repairs of current aircraft, or, if really awesome, to fly newly designed aircraft. From what I see, this is not a standard issue piece, but if authentic to a military member, may be a jacket bought and altered to commemorate a specific assignment or deployment or duty station. If not authentic to a military member, this could just be a jacket that was produced by some company (AVIREX) to appeal to the military-loving crowd that he liked and bought, in which case those patches would simply be decoration/marketing for appeal to the average consumer.
Upon further inspection: no military jacket would have Mig 29 on it. No flying crew, especially on active duty, would have any sort of identifier to their type of craft while in operations. Furthermore, no American crews OTHER THAN TIP OF THE SPEAR FLIGHT TEST CREWS were flying Mig 29s back then. BUT, if your uncle was a no kidding test pilot, he could've been flying a confiscated Mig 29 for the air force to dial down flight maneuvers and capability to train air force pilots to combat the Migs. Again, not too terribly likely. A nice touch, though, is the American/Russian "Please take me to the American Mission Moscow" flag on the lining of the jacket, something that a lot of pilots get sewn into their actual flying jackets incase they're downed inside of enemy lines and need to communicate to the non-english speaking locals. But, again, we weren't flying Mig 29s INSIDE or NEAR Russia. I say all of this to say: it likely wasn't an issue jacket, and unless your uncle was a no kidding test pilot, it is likely just a jacket branded to appeal to the fly boy civilians. There's probably no doubt it is an authentic AVIREX garment, but not an issue piece.