Can’t be for certain, but I think you are on safer ground in the UK with the recent legalization of online gambling. BTW, there is nothing specifically banning affiliate webmasters in the US, and the general belief is that it is completely legal at this time. It is also not against the law for US citizens to gamble online except in certain states where it is expressly prohibited.
There are certain rules and procedures that online gambling sites located in the UK have to follow because of the recent regulation, and some of the affiliate programs have sent out communications regarding this, but not sure how these rules apply to affiliate webmasters.