'Fire away' is relatively common, I'd say, particularly among older people. Luuka looks quite young, which is probably way he hasn't heard it much within his peer group in the UK, but I think it's used quite a lot. It's more idiomatic than 'Go ahead', which restricts its usage. And, unlike 'Go ahead', which can be used in any situation ('Is it OK if I open the window?' 'Sure, go ahead'), 'Fire away' can only be used in a verbal context, meaning 'Sure, ask your questions/ make your suggestions/raise your objections'. It means, 'OK, I'm listening'.

I suppose it depends what country you're looking at. Personally, I don't hear it a lot since I live in the UK, but I'd imagine it's more common in the US. It just means 'sure, go ahead'.