Flight instructor on training flight with student reported a NMAC with another aircraft in cruise flight.

Narrative

We were returning to ZZZ1 from ZZZ where we had been doing traffic pattern and touch and go ops. We had climbed to 2500 ft. and turned to align us to a 45 entry to the left downwind to Runway X. On Foreflight with ADSB in I was watching two aircraft near and below us doing scenic flights. I had heard Aircraft Y announce departing ZZZ and heading south; and saw him on the iPad. He appeared to be heading down the east coast of the outer cape which would put him safely to our left. As he leveled at 2500 ft; he turned right taking him directly over the top of us. We pushed the nose down and had only lost about 100 feet when we saw him overhead. We visually identified him as Aircraft Y on our iPads. I called him of CTAF and asked he knew he missed us by 100 ft; and he replied that I was coming in broken; then obviously changed frequencies as he no longer responded to our radio calls. I See on Flight Aware that he landed at ZZZ2. This aircraft owned by Company. My experience with Aircraft Ys on Company is if they are a Part 91k operator they follow the rules. If they are Part 91 operators; they operate in a hazardous fashion.