Beechcraft Barron pilot reported a NMAC while in the pattern at a towered airport. The pilot stated he was on a left downwind leg when two military aircraft in formation on final approach were given clearance for a right breakout requiring evasive action to avoid a collision.

Narrative

I was flying my Baron from ZZZ1 Northbound to ZZZ2; on an IFR flight plan; and weather diverted into ZZZ under Approach Control. At ~ 10 miles south of ZZZ; my intended weather divert - I had field in sight; I'd gotten ATIS; ATC switched me to Tower; I reported as told by controller about 3 nm southeast of the field for a left Downwind to Runway XX. Before that - I asked for winds as the ATIS called gust 12 kt. winds at 260 and ZZZ was landing XX. Tower and I briefly discussed a western Runway XY landing but it was short (3000 ft.) so I declined XY and told Tower I would take the left downwind to XX to stay with incoming traffic flows; and report 3 miles. I actually told them I was then 4 miles southeast for left downwind XX. She continually cautioned me to stay east of the field; left downwind. As I entered the left downwind abeam the departure end; the ATC controller cleared flight of two L-39's in close formation to come from their initial point to do a RIGHT BREAK; Flight lead told Tower he was not set up for a Right break; he wanted to do a LEFT BREAK. Tower then switched her instructions and cleared flight for a left break; immediately the flight lead broke his jet (I'm guessing his flight was going at least 250 kts.) directly; co altitude; into me; while on my left downwind slowing to 135 kts. with 1/2 flaps down. I had on the Baron's LED landing lights; 3 strobes; port and starboard nav lights; and rotating beacon; on a white baron with green stipes. I immediately called Tower and told her 'you just broke the jets into me; they're going to hit me; I'm breaking east (to get out of the lead jets way); I called the jet leader and said 'you just broke into me; do you see me; I got no answer from lead; I told I was close enough to be his flight lead above and forward of his right wing. While he was completed his break turn to a 360 heading; I almost couldn't avoid getting hit; he was effectively rendezvousing on me while looking away; I could see the back of his helmet; he was looking right towards the runway. I couldn't get away from him fast enough as I was slowing with flaps down. I ended up 500 ft. away off his wing and slightly high. At that point the Tower controller started breaking down. She sounded elderly; very confused; very rattled; very apologetic; with absolutely no situational awareness; she then commenced apologizing and then she started making excuses; twice saying 'we don't have radar in the cab; we didn't see you; what are you going to do now?; we didn't know you were there; etc.'If you look at the Flight Aware track on Aircraft X; you'll see how hard I had to turn away and climb to get away from the lead; Aircraft Y. Aircraft Z broke late and was south of this 'merger' on downwind. I extended my downwind to let Aircraft Z turn base / final; and both jets land; and then I followed the 2nd jet. Inexplicably; the controller allowed other aircraft in or near her pattern as this group of 3 sorted it out. In my opinion; I was witnessing two L-39's on an enroute stopover to an airshow by flying a military formation to a break maneuver; they were cleared to break right; they pushed a weak controller into clearing them to break left into the established traffic pattern; the controller had no situational awareness; and my passenger and I came with 500 ft. of getting hit by the lead. Only to qualify what I saw; I will state I [have decades of military fighter jet experience]; we always flew formation into the break; the flight flew a great formation and looked 'pretty' right up until I started calling for the leader to watch out for me; as he was about to hit me. After landing; I refueled my airplane; then I walked over to discuss the near accident with leader. I asked him if he ever saw me on downwind and he said 'no; but he was cleared to break left '. I asked #2 if he saw me; he said no; but that 'we could not accept the right break because he was in welded wing'; which was his explanation for whyhe didn't see me. He said 'in formation; all he saw was leader's wing '. The pilots were 'wary' they had caused a bad situation; they were cautious with their words; but the sum total of their dialogue was they felt they were cleared to do what they did; and they did it. They both told me directly they never saw me on downwind and I believe that. I also firmly believe the Tower didn't have any situational awareness on the pattern. I feel blessed by enough experience to know what to expect once the two jets I was watching carefully were cleared to break left; and yet I was surprised I almost couldn't pull hard enough to get out of their way quickly enough. My passenger watched the whole thing; she was scared we were going to get hit; she is not used to seeing closure rates like that; she is not familiar with the 'g' I put on the Baron to break east and away from the L-39. This reminds me of the airshow accident P-39 hitting the B-17 recently. Where were his eyes; before impact?? The flight wasn't at an airshow; they were 50 miles north of ZZZ3. I was mad as hell at them; my passenger was very afraid of what she saw; even more so after we landed. She saw too much of the L-39 coming at us; from the right seat; as we turned right. I wished them luck at the airshow; but they didn't need to practice their breaks at ZZZ into a pattern that had more than me in it.