C172 Pilot receiving flight following reported a NMAC with a Beechcraft King Air that required evasive action to avoid a collision. The C172 pilot reported the King Air exceeding the 250 knot restriction contributed to this event.

Narrative

I was flying a C172S (G1000); single pilot; after departing ZZZ. A VFR flight plan was active; with a route from ZZZ to ZZZ1; then ZZZ1 to ZZZ2; then ZZZ2 to ZZZ. I also was utilizing an up-to-date version of Foreflight that was paired with my recently purchased Stratus 3. The aircraft beacon light was checked prior to takeoff and the switch was in the 'on' position. After leveling off at 4;500 ft. and activating the aircraft autopilot; approximately 20 miles to the southwest of ZZZ on a heading of approximately 219 degrees southwest bound; I contacted Center on 132.500. I reported my position and promptly received approval for flight following; with a squawk code. At the time of level off; I had not observed any traffic near my location. Approximately one to two minutes later; after I had established flight following; I suddenly observed an aircraft on my foreflight moving eastbound. The aircraft was observed to be 400 ft. above me; approximately six (6) miles straight ahead of my course; with a speed reported by foreflight of 276 kts. I immediately deactivated the autopilot in my aircraft. At the same time; Center contacted me to advise of the traffic confliction; and reported the aircraft ahead to be a King Air and I was instructed to immediately turn right. I began an immediate sharp right turn with a moderate descent; and observed the King Air still heading towards me; now reporting same altitude. Center told me the King Air was also descending. I sharpened my turn; and observed the Foreflight indicator for the King Air turn Yellow; as well as the airplane icon approximately 1 mile in front of me. As I sharpened my bank; I observed the King Air on my Foreflight make a sudden sharp right turn; as the position of the aircraft on my Foreflight showed the King Air nearly over top of my aircraft position indication. I never saw the King Air pass by; and Center shortly thereafter told me the King Air was passing behind me. During the evasive maneuver; I had descended to an altitude of approximately 3;100 ft. According to my Foreflight; the King Air had descended to; and leveled off; at 3;000 ft. and maintained 272 kts. approximately 5.1 miles behind me (to the east). Flight Briefing estimated winds at altitude were briefed to be between 20-25 kts. from westerly headings. I thanked Center for their quick assistance and noted the details of the situation the best I could. I am unaware if the King Air had TCAS; and did not hear the King Air talking with Center (unsure if/who they were in contact with). I did make record of the tail number of the King Air; for reference if asked. The airspace is obviously congested. Additionally; thunderstorms and convective activity was both reported and observed to the west of my aircraft's location by approximately 100 miles; moving east-northeast. I estimate during the near miss that the King Air was descending in excess speed in a rush to beat the storms into their landing point that was in the vicinity of ZZZ (the aircraft was later observed in a climb just to the west of ZZZ and speaking to Center); not in communication with controllers at the time of their descent; and due to the positioning of the instrument panel in a King Air; did not observe my aircraft until the near miss or TCAS indication. Continue to promote and allow General Aviation aircraft to utilize flight following with ATC. Also; assertive enforcement of speed limits in known high traffic areas especially while descending. Continue with enforcement and promotion of ADS-B Out and its benefits. I am unsure of the accuracy of speed indications through Foreflight/Stratus; however; they have generally been accurate in regards to my own aircraft information.