I have coached and instructed over 200 boat fliers how to pack their kayaks for flight as the director of New River Academy. We typically fly with a play boat and paddle bundle. And have packed paddles with boats too. Here's how...
A. Brace your paddle on top of your kayak. Your goal is to protect the paddle from breaking.
B. Use your pfd, thermarest, shoes, sleeping bag, anything with support to fill the space between your paddle and boat on each end.
C. Secure, secure, secure it. Clear packing tape is better and cheaper than duct tape in this case. Get your "baby" snug and fit to your kayak.
D. Test your paddle wrap... Can your boat fall upside down onto your paddle blade?
E. You don't have to have a boat bag. As a matter of point I really dislike them because I travel internationally for months at a time. A boat bag is an awkward piece of luggage. I like the idea of having a disposable boat wrap. Tarps also can serve many other purposes: ground cloth, dish drying area, dry area for roadside truck camping, kitchen rain protection, and they are practically disposable.
Boat WRap Goals: to protect your boat from airport abrasion and to hide your "kayak" label if you are trying to get a "surf board" rate.
Easy things you can wrap your kayak with that are disposable:
tarp and blanket. I once bought a $2 blanket at a thrift store in San Jose Costa Rica.
Oh.. here is an article I wrote a few years ago.
How to Fly with Your Kayak
Owner- Pucón Kayak Hostel