I don't see why a UK national couldn't be a policeman in Spain in theory.
However, in practice I would say it's almost impossible. You would need fluent spoken and written Spanish. Also, for any functionario job like this in Spain, you have to sit a super competitive entry exam called the oposiciones. With unemployment at 26% and youth unemployment at nearly 60%, there are a lot of people studying for these exams. I know people who have studied for years and years to try and get a functionario job but have failed because of the competition.
Sadly, a functionario job is a dream job for most Spaniards as they are the only jobs that are secure these days.
I think your 16 year old son is best off becoming a policeman in the UK...