BRM15

Born in the UK in 1998 to two American parents in the UK with the US armed forces. Has a long form birth certificate if that matters. Is this person a UK citizen?

BritInParis

Probably not. Automatic birthright citizenship ended in the UK on 1 January 1983 so in order to acquire British citizenship by birth anyone born in the UK after this date either need to have a parent who was themselves a British citizen or was 'settled' in the UK. Visiting US military personnel are unlikely to fall under either of these categories.

If the person concerned lived in the UK for the first ten years of their life then they can apply to register as a British citizen however I would think that also unlikely.