I’ve noticed this too, I definitely seem more attractive to the opposite sex when in a relationship. When single it seems much harder work.
IME flirting is easy when you know your bluff isn’t going to be called. If you have a Mrs I think you tend to just carry yourself with a bit more confidence.
Of course, if you’re so inclined you can flirt away without fearing that you might be rejected. If you are rejected, well it doesn’t matter does it. You can tell yourself you were only messing around anyway, bit of harmless fun, and you were always going home with your Mrs who you love very much and don’t need anyone else, thank you very much.
If you’re single you’re flirting with a mission, and if you’re rejected it matters because you go home alone. The stakes are high and the nerves kick in.
Plus as stated above, if you’re in a relationship it sends a message that you might have something to offer. Bit like applying for a job whilst in a job, vs applying for a job whilst on the dole.