I ran a test with FlightGauge which polls for data just like FlightMap. It gets back just a little less data but I calculated that for an hour of usage the data between FlightConnect and FlightGauge is around 6mb. I'd guess FlightMap is a little more than that probably in the 10mb range. So you can cut around 10mb per hour off the numbers in my previous post as this 10mb would not affect internet bandwidth but would be local wifi bandwidth.

So based off my testing 1 hour of FlightMap usage would yield:
~10mb per hour local wifi bandwidth usage
~50-70mb per hour internet bandwidth usage