I had several paintings of mine that I unstapled from their stretchers, rolled up and put in my suitcase; they all fared well but they were acrylic on canvas. Acrylic paintings are so tough you can roll them. I have not had them restretched yet, however, and so cannot tell you what it might cost for that service.
But I would not do that (remove from stretchers and roll up) if your painting is oil on canvas.
If it is, the only advice I can add is NOT to do what I did with the one oil painting I had. Although I left it stretched and did not roll it, I shipped it with my ocean freight shipment but I did not protect it properly from things I packed it next to, things I wrapped it with, and from the inevitable heat it was going to endure by crossing the Gulf of Mexico in July (!!) Result was that when it arrived and I unwrapped it, the paint had wrinkled in places, and in other spots a kind of in-place melt-then-reset had clearly occurred because of the high temperatures the shipment had been through. The image is still okay actually, just the surface texture that has suffered.
It doesn't sound like you plan to put your painting through a two-month shipping journey, just the plane, but if it's oil make sure you get some pro advice about what to do with it. If happens to be acrylic, you can abuse those quite a bit and they will be fine.
