I am married and in an FLR. I do not want to be a cuck and my wife has no interest in this as well so there is no problem. Many submissive men get off on being a cuck. Some of them are bi and will give oral sex to the cuck (so they say online).
I assume you don’t want to get divorced. You say you have discussed it with her a lot and she still wants it. If you want to continue the FLR marriage then you probably have to accept it. Your other option is to tell her that this crosses a line and you won’t accept it and then see if this leads to separation or divorce.