What is the role and historical context for "come" in "Kingdom come"? I've heard this said before but it seems to stick out grammatically. Is it correct?
It's an archaism: it isn't grammatical in 21st century English to say "(thy) kingdom come" but a few centuries ago it appears to have been more common. Functionally, it is often similar to using "let" as in "(Let) thy kingdom come".
From this phrase, "kingdom come" has effectively become re-analysed as a compound noun meaning something like 'a long time in the future' or 'the beginning of the next world', mainly in the phrase "till kingdom come".
It's a quote of the Lord's Prayer in the Bible: "Thy kingdom come, thy will be done ..." It is meant literally: "come" has the conventional sense of "arrive" or "get here". It is being used in the imperative, in this case in the from of a request. It's the old Jimmy-English so the word order and punctuation are different from conventional modern English usage. In more modern English it would be, "Please make your kingdom come", or "Come please, kingdom", or, "Please send your kingdom to us."
There is a rather obsolete idiom that goes something like "I may have to wait until kingdom come for this!", meaning until God's kingdom is established and history as we know it comes to an end, i.e. for a very long time. It's not good grammar, it would make more sense to say "until the kingdom comes". But that's how idioms are. Anyway, unless you're reading an old book, I doubt you'll see that, I haven't heard it in years.