I get spam in gmail. gmail spam has nothing to do with the browser. The spam mostly goes right into the spam folder. I opened gmail accounts for my kids and within 3 or 4 days, they had spam, complete with f-bombs in the subject lines, that didn't go in the spam folder. So needless to say, they don't get to use their gmail accounts.
Chrome is a nice browser but it doesn't have any better security features than firefox.