[subject] + 尽管 + [verb phrase]
有 + [noun] + (,)+ 尽管 + [verb]
尽管 before a verb invites someone to do it freely, with no need to ask or feel awkward. It's spoken, and almost always an offer to the listener.
A common frame is 有 + noun, then 尽管 + verb: "if there's anything, just…".
尽管放心 is a set reassurance, "rest assured".
尽管 also means "although", and the two are told apart by where they stand. "Although" opens a clause, before the subject, and a second clause with 但是 or 还是 follows. "Feel free" sits after the subject, right before the verb, and the sentence can end there.
尽管 encourages an action, so it doesn't take 不 or 别. To tell someone not to worry, use 尽管放心 or 别担心, not both.