It's a frequent topic in this place, ( so use the search function), it's a topic that comes up fairly frequently, usually as a scare story, in the main stream media (so Google is your friend), just be careful, you need to filter out the sensationalist junk/tinfoil hat material from the vaguely objective stuff..
There are lots of variables involved in how much radiation you are exposed to on a flight, mainly tied in with state of the sun's activity, ( e.g. sunspots, solar Flares, particle events, and also the strength of the Sun's magnetic field, which protects us from cosmic radiation..).
Three simple rules:
Longer the flight - more radiation;
Nearer the north or south
magnet pole - more radiation;
Higher altitude - more radiation.
IMHO there's plenty of things about flying that can be as "harsh on the body" if not more so than exposure to radiation at cruising levels - I'm thinking time zone changes, irregular exposure to daylight, lack of and disruption of sleep, irregular eating habits, possibly poor diet, dehydration..
https://www.faa.gov/data_research/re...media/0316.pdf
https://www.cdc.gov/niosh/topics/air...radiation.html