How old do you have to be to drive with a farm license plate?

Depends on the class of vehicle. While registered farm vehicles are not jurisdiction of the FMCSA, and do not require a CDL, states still have their own licencing requirements for vehicles over 26,000 lbs. GVWR which are exempt from CDL requirements, and you'll typically have to be 18 or older to operate them if it's a class of vehicle which can't be operated with a regular drivers licence. But, for something like a pickup truck with farm tags, the age requirement shouldn't differ from what it would be for a pickup with regular tags.