I am self employed, and am registered with HMRC under my name and not a business name.
When contacting them for an enquiry about changing my business I was told I wouldnt need to because as the VAT registration was in my name I could just claim any VAT paid in my name as normal. I for just about anything I get charged VAT on, provided I can say it is in someway connected to my job as a courier..
You CHARGE Vat on services rendered, ie as im a courier, a delivery job ive done, and I CLAIM Vat back on services that I have used, ie someone invoicing me, the difference goes to her majesty's coffers - I dont really see how flight costs would fit in here
I would try contacting HMRC for clarification but I think unless you have a business or are self employed with a trade (not just self employed because you can etc), I think you would fall at the first hurdle of registration!
www.hmrc.gov.uk
regards