The story I'm working on opens in 1942 with my characters going into captivity but the plot and story don't really get going until 1945. The time in between this has no real bearing whatsoever and ideally I'd like to jump the three years at the start of a chapter in a single paragraph. Is that the way to do it or is there a recommended / acceptable way to jump a few years in a story?
You can jump the time period - that happens all the time. Another way to do it is to start in 1945 where the story "gets going" and then flash back to 1942 if the story requires it. If the only thing the reader needs to know is that they went into captivity in 1942, you can just refer to that in the story.
How much of the story happens in 1942? If it isn't a lot, perhaps a prologue is called for? I like the flashback technique too, if it isn't done so often in the story that the reader gets lost. That might let you parse out information more effectively to build suspense in the later story too.