You can look at the current activity charts and extrapolate from the particle flux, but it's likely going to be below 1mSv for a 6 hour flight. The XKCD radiation chart provides the most sensible comparison for most people I think:

https://xkcd.com/radiation/

As a comparison, a typical flight might only have a dose of 40uSv, so like 25 normal flights. But still many people take many more trips than that.

FWIW I'm an aircraft mechanic and the only complaint I've ever heard related to solar storms was that the HF radio stopped working. Which isn't a radio thats going to be used or even installed on a typical airliner.

Although it could also disrupt satellite communication causing some delays in flight planning and aircraft/crew turnaround.

For a fun anecdote, when the HF radio fault was reported we weren't aware of the troubles in the ionosphere. After a few hours of troubleshooting on the system and not finding any problems I flippantly remarked that it must've been a solar flare because the radios perfect. 15 minutes later I was reading the news and saw the headline.

HF is installed on many airliners, it's mandatory for the North Atlantic routes between the US and Europe. Still checked every flight as a backup to satellite position reporting (which is relatively new)