What is the correct action to take when I find a question that could be migrated to another SE site, which isn't on the list of sites I can pick using the close dialog?
Should I flag it for moderator attention and vote to close as off-topic or just do the former?
I worry about off-topic questions remaining on the site if the migration flag is rejected, although I suppose a moderator is likely to close the question outright in that case?
Unless you're a regular user of the proposed target site (i.e. you have about 1000+ rep there) then it's best to just vote to close instead. Often just because you think a question fits better elsewhere doesn't actually mean it is a better fit. (Even if you're well meaning, each Stack Exchange site is different and cater for different types of questions more or less so than others, so they all have their own quirks).
However, if you're a regular user of the other site and you know it's a better fit then flag it and say that you're a member over there and that it's the sort of question that works well there.
Speaking as a mod on one of the StackExchange sites: https://ux.stackexchange.com/ we get get quite a few flags for migration from people who aren't actually users of the target site but believe that it's a good fit for it (usually it's StackOverflow they're suggesting it be moved to). They're usually well intentioned flags, but often not appropriate for that site.
Also, please don't leave a comment on the question saying "This is a better fit for X" site because that might encourage the user to cross-post their question to other sites and risk getting it closed off there too, which annoys both the target site and the poster and it ends up with loads of comments along the lines of "well I was told by X site that this is a better fit, but now you're saying it isn't!"
So yeah, flag it if you're a regular user of the other site, but just vote to close if you aren't.
Argument for voting to close: Questions are only migrated if they are off-topic on the source site. Moderators prefer to let the community decide whether a question is on-topic, so they may be reluctant to migrate a question if it doesn't have close votes already.
Argument for not voting to close: if the question gets closed (which is likely on Stack Overflow, at least in high-attention tags), it creates more work for moderators, because migration is only available from the close dialog.
On Stack Overflow, I tend to cast a close vote when there isn't one already and not to cast a close vote when the post is already in the close queue. On other sites, where moderators don't handle hundreds of flags a day, I just do the right thing: vote to close if the question is off-topic. I'm happy to change my behavior if the SO mods prefer it one way or the other.
In your flag, it's best to indicate how confident you are that the question is suitable for the other site. Are you a regular there? Or do you just think that the question may be on-topic? If you aren't sure, check at least the target's site's about page and its help/on-topic page before deciding whether to request a migration.
Note that questions that are more than 60 days old can no longer be migrated, so if they're off-topic, just vote to close.
