Does anyone in the UK say flat building? I live in the US, mind, so I have no clue. It sounds a bit funny saying that. Do they say apartment building instead, maybe? Or is there another word for a whole building of flats?
In the UK, you would probably say a block of flats, or -- especially in the case of public housing -- a tower block or high-rise, if it was more than about ten storeys tall.
If you perform Google image searches on those terms, you'll get a good idea of what they represent.
I've never heard an apartment building being referred to as a 'flat building'.