I am NOT an expert in VAT but I have been "doing it" for many years, and operating a small entity that is VAT registered.
If I provide consultancy services, I have to pay VAT on my outputs, so I add VAT at the going rate to my invoices. I charge on an agreed basis to the client. Very often the basis agreed is for a rate or possibly a fixed price, plus expenses. The expenses could be travel or accommodation or materials. Some of these inputs are standard rated, some zero, some special rate etc. However, I was picked up many years ago by HMRC that because my outputs were VAT rated at the standard rate, that ALL invoiced items needed to be charged at the standard VAT rate. My busness was the provision of consultancy services, NOT travel accommodation etc. So I charged std rate on expenses, no matter what. [It does not matter to my clients as they are also VAT registered, and claim back all their input VAT].
Transfer all that to an AA charity: for the majority in the UK I believe that most still have their helicopter operated by a commercial operator. That operator will be registered for VAT, and will charge VAT on all his outputs. My guess is that it depends what service the operator is registered as providing. If he provides commercial air transport, then he will have to charge standard VAT on all outputs. If he had his services to include the provision of aviation fuel, then maybe he could charge 5% VAT on the fuel.
We need an expert in VAT.......... However, we are only talking about 5% for fuel if that is separated out.