I do have a British birth certificate, but as far as I know I only have one crinckled copy and the concern is what might happen if that were lost - are we (foreign born forces kids) in the wider system as we think/assume we are?
As to your son being an NCO, as I said there is at least one of the Windrush-related cases that served several years in the army. Seems that in itself is no protection.
The US immigration issue is true - I have always had to say where I was born and not where I was from. As both have been EU nations subject to the same rules it has never been an issue, but who knows if that will remain so.
While clearly nothing to do with Brexit and Windrush, this does lends itself to the wider point about confusion that officials can sometimes have in discerning the difference as to place of birth and nationality. Its the US today in this particualr instance, but why wouldnt it be the UK tomorrow?