What's the best way to treat a migraine from a neck tattoo?

Neck tattoos neither cause nor trigger migraines, assuming no local infection. Since numerous potent medications can prevent migraines these days, see a neurologist and get this addressed. Other triggers may be managed.

Since neck tattoos don't cause migraines, your question should be how to treat migraines, period. First thing you need to do is see your doctor to find out if what you're calling a migraine, actually is, rather than some other kind of headache. Only then is treatment considered.