Brickhistory is correct about the US Space Badge. It's also been known as Buzz Lightyear wings since they're almost identical to those on the cartoon character. It was a feeble attempt to make the space professionals more important by making them look more like pilots. Many that I worked with disliked the pilot similarity because they take pride in what they do and don't feel the need to be associated with someone else for respect.
The most likely reason he's wearing the foreign badge is that he's earned it. RAF Flyingdale functions as an integral part of the 21st Space Wing, at least according to the 21st. Look at the list of subordinate units on this page:
Peterson Air Force Base - Units It takes a careful inspection to find that only one token American is actually part of the 21 SW.
It looks like the only downside to the cooperation between air forces is the sharing of excessive uniform trinkets, making the British look almost as bad as us.