Pilot reported efforts to avoid traffic resulted in taking evasive action and a NMAC.

Narrative

I was flying South along the ZZZ shoreline following the ZZZ VFR flyway and on flight following with ZZZ Approach. On my EFB I was able to see traffic at my same altitude approximately 7 miles South of my position flying toward me. I began to adjust my route to the right to avoid a convergence. As I adjusted right the aircraft approaching began turning more to the left; in other words turning toward me again. I made additional adjustments to the right; having to be careful of the city which was further to my right as I was now approaching the pier. However; the approach aircraft continued turning further left; persisting the potential conflict. It was at 5 miles separation that ATC alerted me to the traffic. I stated I did not have a visual but was looking for them. I continued using the ADS-B information in my EFB to maneuver to a flight path that would avoid the traffic but not send me into the city. As we approached 2 mile separation I received instructions from ATC to immediately turn left to 090. I complied immediately while also increasing to full-throttle and initiating an aggressive climb. In the turn now; belly up to the conflicting traffic; I finally caught sight of them as they were now making an aggressive left banking turn away from me with only about 500 ft. of lateral separation at at my same altitude from what I can tell. This is later backed up by viewing historical ADS-B data found online. I noted the tail number; Aircraft Y; which I later found to be registered to ZZZ flight school. Looking at the track of this flight and past flights for the same aircraft; it appears to be performing their downtown flight".This incident highlights some key issues I feel should be addressed. Part 135 flights (which I would assume this to be based on the description on their website) using a highly congested and narrow VFR flyway for such operations seems inherently dangerous especially on busy weekend mornings. Had the other aircraft been in contact with ATC I believe this situation would not have occurred. Again for a commercial flight operation to be conducted in this space without contact with ATC seems exceptionally irresponsible. The other pilot's failure to properly yield to the right for head-to-head traffic persisted the conflict resulting in the near miss. The VFR flyway does not provide any form of separation (altitude or lateral path) for traffic moving in opposite directions. If different altitudes were specified for northbound vs southbound traffic or different tracks were provided I believe it would make this flyway safer. There is no common traffic frequency in this area. If; like on the Hudson River corridor route in New York; pilots were required to make position reports; perhaps on a common frequency or to ATC; it could again make this flyway safer. Fortunately; between I and ATC we were able to resolve the conflict without a tragic incident. I'm personally frustrated that a flight school operation is conducting commercial flights such as these in what I consider to be an unsafe and irresponsible fashion."