I think your channels might be too narrow. Ribbon conveniently folds onto it's self to pull through a small channel but for the elastic you need to allow for the width and thickness of the elastic as well as how thick and cumbersome your fabric is. Not to mention if there are any seam allowances in the channels, both running the length or perpendicular. I'm guessing a bomber jacket isn't thin slippery fabric.
Are you channels at least ½ inch wide? I hate to ask but are they sewn straight, no narrow spots? They can snag things up.. Also, on something like this you can't feed one through and gather it to spec unless the channels are very roomy. It renders the others impassable. I would be threading all three through at the same time to help keep them even.
Oh. I always use a bodkin with 100% excellent results. My favorite has a safety pin type latch at one end and is heavy wire, rounded at the other end. It's about 12 inches long, bought in the 70's. I have other more standard ones for general use and resort to a giant safety pin sometimes with extra wide elastic