In the last 90 days, there have been a grand total of one question migrated from Aviation to Travel. There have been 3 questions migrated to Aviation (from Travel, IT Security, and Electronic Engineering) which have all been rejected. (If you have 2,000+ reputation, you can see the list in the moderator toolsmoderator tools.)
I know that this is a bit of a Catch-22, but we don't add a default migration path when there aren't a fair number of successful migrations already. This is doubly true for beta sites. For the philosophical underpinnings, please read Respect the community – your own, and others’. The key takeaway:
As members of a community, your first loyalty should be to that community. When evaluating a question, you shouldn't be looking to push it off on some other site; instead, ask if it could be appropriate and on-topic for you, the experts who the author decided to ask. Be a bit jealous of your site—don't blithely turn askers away simply because their question could be asked somewhere else. Don't hit them over the head with your scope, help them tailor their question to fit into it—and if that means your site’s scope overlaps a bit with another site’s, so be it.
If you do find a question that's not relevant here and would be ideal for another site, just flag a moderator with the "other" reason and explain why it belongs elsewhere.