Not all that easy, normal dosimeter patches are not suitable. You need kinda special equipment for that, which is of course available, just hire a scientific institute that deals with stuff like that. I know Lufthansa did that quite a few years ago, they hired the
PTB to measure cosmic radiation and proposed countermeasures on delivery flights (if i remember correctly 744 deliveries).
The 787 could suffer higher radiation though, if it flies consistently higher than other planes.