"If that's the case, I might as well ask Ignatius to be my husband. A wife in England, a husband in Faerie, I'm certain there's some arcane fae law that allows it. Besides, we both know there have been worse rumors spread about me!"

He's joking: Strange knows full well that neither Ignatius nor Arabella would consent to such an arrangement (and what Arabella says, Strange will do). He's matching Childermass's smirk with one of his own as he gives the man a little shrug.

No comment on that LeFlamme thing, mostly because Strange, in all his selective obliviousness, didn't exactly realize that.