The mechanisms by which I check if a username is taken on this page are pretty rough and ready.
I don't use APIs to check availability - instead I check the page response for a site - so e.g. if I visit example.com/username and it returns an error to say the page doesn't exist, then I assume the username is available.
This method isn't at all foolproof, so just because the results say a username is taken, doesn't mean it really is. For example, I've found out that some sites don't make deleted usernames available for re-use - such as Tumblr. Therefore on some username checks, the result says the username is free, but when you try to sign up using that username, it says it's taken, because someone once used it, and deleted it, and it can't be re-used.
This is a bit of an essay, but I just wanted to say that this is a rough and ready checking system.
You can double check the results from this page against other username checking sites, such as: