I had exactly the same problem after downloading the new IOS 8.4. Went to Apple Store twice (2nd time got a new phone), and made a call to Apple support once. Was told I needed to completely "reset" the phone--did this 3 times. Couldn't get them to acknowledge that the flashing calendar events was a problem. It was using my DATA plan also! Finally went back two years in my calendar--they were not flashing there. Deleted each and every event that was duplicated, then shutoff duplicate calendars (birthday and personal). This stopped the flashing events. Wish I could give a better explanation on the duplicate calendar events but this fixed the problem with flashing, data usage, etc. Have a new phone anyway!
