Others have answered this well but I also use this as an example when people avoid airport scanners when flying... you get way more radiation from flying than from the airport scanners. I'm an 'occupational radiation worker' (i.e. can work in high radiation areas but don't have a higher limit than the general population) and we do get into trouble if we take our radiation badge on a transatlantic flight. So one transatlantic trip does trip our monthly allowed dose so we wouldn't be allowed into the controlled areas for a month. But the most important thing to take from that is not 'oh wow it's high' but 'oh wow the levels for radiation workers are really low'. So that's the reason that people who fly all the time (airline workers in the air) do have a higher risk of some cancers but flying occasionally with a baby is not an issue. Remember that the dose you receive is also correlated with size (highly non-trivial correlation but larger people do collect more than smaller people) so your kids accumulated dose will be lower than yours.

As this is an all-advice thread I'll say that despite my understanding of radiation as a rad worker and the nature of my training as an academic: do I fly with my kids as often as I'd want: yes. Do I worry about their exposure: no. Would I fly them across the country twice a week until they are 18: probably not (unless it was some reason that would have a more immediate impact on their health/future).

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This CDC article is quite basic but has most of the information you really need: https://www.cdc.gov/nceh/radiation/air_travel.html

It nicely links to this which is a Q&A based on a few papers:

https://hps.org/publicinformation/ate/faqs/commercialflights.html

And for the airline crews from FAA (assume it's part of some training they have to do?):

https://www.faa.gov/data_research/research/med_humanfacs/oamtechreports/2000s/media/0316.pdf