If you're planning to cook on base, you won't have many problems moving from place to place. Off base rules may seem to vary quite a bit from state to state, but most are pretty similar. You can cook on almost anything under most states TFE (temporary food establishment) regs, but these are usually reserved for fundraiser and fair type activities. Beyond that, to set up and sell at will to the general public, most states either require you to have a fully equipped mobile kitchen, or work out of a commissary. NC does not recognize "mobile kitchens" so a commissary would be required. The commissary could be a restaurant you have a rental arrangement with. How closely that arrangement is examined will vary from local to local.
Finding enough customers to make it worthwhile is the hard part. Jobsites and businesses frequently have contracts with food trucks, so they're a non-starter. Fairs/festivals have steep up front fees, and they can be hit or miss. Nothing like paying out $5K for a fair only to see it rain for 7 days.
Also, most events have menu restrictions with regards to competition among vendors, so you might not get in cooking BBQ. I know some events that have waiting lists 20 deep with wishful BBQ cooks who have waited years for a slot. And setting up around town like you see on TV will force you to run the gauntlet with every restaurant within miles, even if it's legal, and in most cases it's not. You are the enemy.