C-182 Flight Instructor reported an NMAC event during a training flight with two high speed military fighters which flew within two hundred feet of the training aircraft. The Instructor immediately took evasive action to avoid a collision.

Narrative

Me and my instructor took off from ZZZ around XA:04 on Runway XX. After following the noise abatement procedure; we fly almost direct to ZZZ1; as we are getting close to the waypoint ZZZZZ (~XB:17) we turned right for a little to avoid a traffic coming from ZZZ1. Not long after our turn; we immediately saw 2 hornet fighters blasting heads-on towards us on the left; my instructor immediately took evasive action by going down and bank the aircraft left after they passes as there was another fighter immediately passed us on the right. (looking at the Sectional; they probably were on VXXX towards ZZZ2 VOR) It all happened in a few seconds. It felt like a very close call; we were probably only a few hundred feet away if not less. On the communication side; after we took off from ZZZ; we got in touch with Approach as we're heading towards ZZZ3 and that is the nearest box for Approach frequency. We requested a flight following to ZZZ3 and Approach just assigned us the squawk code. The event took place right after I put in the squawk code to the transponder and Approach asked us if we saw the hornet fighters right after the event. We discussed the event with the ATC once we cleared the area and the adrenaline settled down. According to them; the fighters were on Center frequency while we were on the Approach channel hence they weren't able to give us a heads-up before it happened. We also did not see the traffic coming; they did not show up on the ADS-B traffic display and considering we were right on top of the lake; we probably were not in range of any ADS-B ground station and/or the fighters did not use Mode-C/S transponders or ADS-B out. Reflecting on the event; we should've been more careful when choosing the frequency we talk to as the ZZZ A/FD does specify Center for Approach.