I have a similar question. Not to create a fork, but how to maintain my own patches on top of chromium (and not have to host my own version on github, that would take ages). How can I make it easy for contributors to fetch the official chromium source, patch it with our custom patches (which I don't know how to make) and continue development (to make more patches)?
And to answer your question:
Even if you somehow managed to git push, what happens when chromium comes out with an update?
And yes you'd use git clone to get your fork and fetch to get the official chromium fork.