If I worked for BA, it wouldn't be hard for me to at least to attempt to find this seller.
I know that this person has 255,000 miles in his/her account. I may assume that he/she could have rounded down. I see the seller is possibly based in Cheshire. With the seller mentioning Tesco vouchers, then this person potentially has had a large transfer from Tesco — and possibly no other transactions.
Does BA keep a list of previous destinations people have searched for? If so, I'd look to see if my list of suspects have done searches to Florida. Possibly MAN was the origination point if they live in Cheshire.
I would also have a shot at searching for 'js2955' to see if it can be found in any email addresses. I may also assume that the person's date of birth could be 02/09/55. By using JS in the username, the person's name could be Jason, or it could be their initials.
If I found a few matching accounts, then I'd keep an eye on them and look out for any suspicious activity for third-parties and then BOOM, gotcha! Gosh I should be a detective!