Can EMT's carry firearms

Yes, mostly for their own protection

But, it is only legal if the person otherwise qualifies to carry a firearm. EMTs (assuming you mean Emergency Medical Tech) are not normally sworn law enforcement officers, therefore, they cannot legally carry a weapon just because they are EMTs. They must carry in accordance with state law, whatever that is. However, I doubt any city in the U.S. allows its EMTs carry firearms. I know that MOST cities don't.