Cessna 172 Flight Instructor reported an NMAC event that was caused by an ATC assigned heading. Flight Instructor executed an evasive maneuver to prevent a collision.

Narrative

Toward the end of my hour and a half flight block at ZZZ; my student and I were transitioning back to ZZZ from a local airport (ZZZ1) where we conducted practice landings and maneuvers in our designated practice area in which we were ramped out by dispatch to. We called 10 NM northwest and told ATC our intentions. They instructed us to report back 4 NM northwest; we complied. Upon reaching approximately 7 NM northwest; after several broken radio calls that my student and I were unable to distinguish; we were instructed to fly NE in order to provide separation for a flight of military T6's that were on a long straight in final.I confirmed that ATC wanted us to fly northeast in order to avoid an aircraft that was on a straight in; they confirmed. Making a judgment call; I decided to instruct my student to fly straight north due to not wanting to cross over; under; or in front of the approaching aircraft that were seemingly on a straight in long final. Being out of the class D airspace; I was free to do as I pleased to ensure safety of flight. We called ATC and informed them we were doing so; unsure of what they wanted us to do; as we saw on our Multi-Function Display (MFD); the indication of an aircraft -2 (200 ft. below) moving toward us at a fast rate. ATC informed us that there was no traffic to the northwest; and that they were on a straight in. To which I responded they are incorrect because I have two military T6's in sight (visual; and on my MFD) and they were passing below us approximately 200 ft. below. We then turned to the left (west trending south/southeast) in order to keep the T'6s in sight and continue in to the airport.