IFR Cessna with JAX Approach experienced a conflict with a flight of two antique military fighter aircraft; unreported by ATC; noting a similar conflict with unreported traffic during a previous flight with Daytona ATC.

Narrative

ATC gave me a descent from 5;000 to 4;000 [and] during the descent at around 4;500 I looked out the right window to see two antique military aircraft in formation coming right at me; I pushed the nose down hard. The distance is a best guess; but I was close enough to be able to read the name painted on the front of one of them. After the near miss; I immediately queried Jacksonville Approach about the event; asking if they showed them on RADAR. The Controller responded saying they had no targets on the scope around me not even a primary only. I do find it hard to believe that 2 planes in formation wouldn't show on RADAR. I had another problem a while back with Dayton Approach flying on v267 abeam DED; a Cessna preformed a spin on the airway; I banked hard right and pulled away; the pilot of the Cessna recovered at my altitude on a collision course. Had I not pulled away; we would have collided; I was on an IFR flight plan; I asked Daytona if they had that plane on RADAR; the Controller advised that he had primary only on him. It is my understanding that if I am IFR; and there is a primary only in front of me; ATC is supposed to advise.