If you're thinking of sales tax (i.e. the US equivalent of VAT), then no, because you are paying a sales tax on a service based in that country.
If you purchase goods in the US and bring them back to the UK, you reclaim the sales tax at US customs on departure (after getting a form from the vendor) and pay UK VAT on arrival. Probably doesn't pay you to do that!
If you're thinking of reclaiming the training costs against your previously earned income and tax thereon, that's a no-no with regard to UK tax legislation. If you are going to be a freelance, self-employed pilot, then you would need to seek the advice of a qualified accountant as to whether you can reclaim the training costs again future income as a pilot. However, my understading is that these are not allowable.
Cheers
Whirls