Flamingoes stand on one leg. His wife told him to do something. He put his foot down. Figuratively, this means that he was firm with his wife. He is not going to obey her. Literally, he put his foot down on the ground. So he stopped standing on one leg. He stopped impersonating a flamingo. He obeyed his wife. It's a pun. There's no point where you laugh. It's not that kind of joke. You more groan and smile. It's quite lame.

It isn't that funny, in fact. Flamingos seem to like standing on one leg (or foot). Apparently they can sleep like that to stay warm. On the other hand, the expression "to put one's foot down" means to insist that something stop. A typical example would be when children are playing loudly and mom is tired of the noise she might put her foot down and stop this. In other words use her authority as a mother to get the children to play quietly. So here the husband had to put his foot down to get his wife to stop telling him what to do (or something like that). She thinks he is acting like a flamingo, maybe because the husband is loud and calls attention to himself, rather than standing on one leg? Somewhere in there is a joke I guess!

wikipedia => Plastic flamingo some people just start laughing when hear other laugh

Understanding puns is difficult in a new language because it requires familiarity with expressions that make no literal sense. I thought your joke about the flamingo was funny. My wife and I both laughed. She made up one of her own: Question: Why did the turtle not fly? Answer: Because he did not want to go out on a limb. A request for "animal puns" at AI will give you dozens. Here is one I found there that I find funny: Question: Why did the chicken go to the seance? Answer: To talk to the other side. Get it? That's a particularly hard one because it requires not only that you understand who one might be talking to at a seance, but also that you be familiar with other jokes about chickens.