Existence of "multi" in US English

Solution 1:

You were already given this answer by several of the comments, and it's already implied in polynym's answer, but let's make it explicit:

Yes, the prefix multi is valid in American English, and usually used unhyphenated. You can see dozens of examples on Wiktionary or Merriam-Webster. If your grammar and spelling checker fails to accept it, it should be overridden manually.

Solution 2:

For clarity, I often use a hyphen for some multi- words: multi-threaded rather than multithreaded.

That is accepted by the spelling checker in my current browser where without a hyphen it is underlined in red. There may well be a discussion about appropriate use of the hyphen; I tend to use one as seems right to me and not according to some arbitrary rule.