By saying "my flow is super regular," this character, Jaimé, means that he has bowel movements very regularly and frequently. He therefore uses the toilet often, which in turn makes him especially appreciative of his partner's Toto toilet. (The underlying premise is that Jaimé's own toilet is an ordinary American one that is much less pleasant to use.)
Jaimé has just admitted to his partner that he is a hoarder, and that this is why he has always insisted on sleeping at his partner's apartment, rather than inviting his partner to sleep at Jaimé's apartment. But then he adds that there is a secondary reason – he really likes his partner's fancy toilet, because he moves his bowels so often. This is supposed to be funny because 1) this second reason is so trivial compared to the first; 2) having such a strong preference for one toilet over another is a bit silly; and 3) alluding to bowel movements in such a moment would be very inappropriate.
Additionally, I guess "my flow is super regular" is supposed to be a funny way of saying "I have frequent, regular bowel movements." It's not a common way of saying this at all, but in this context the meaning would be clear to most native speakers. In American television comedies, unusual idiomatic expressions are often used for humorous effect.
And finally, as @Michael Harvey has noted in a comment, this particular biological function is widely thought to be funny in and of itself, so that merely mentioning it can be an easy way to get a laugh. The English term for this kind of humor is scatological humor, and the term is often though by no means always used in a disparaging or disapproving way. That is, it is often used to dismiss jokes like this one as unsophisticated or vulgar. (For what it's worth, I have nothing against scatological humor but don't think this particular joke is funny at all.)
I'll also clarify a few other points even though they aren't what you're asking about: First, the main language spoken in Mexico isn't called "Mexican," it's called Spanish (or Mexican Spanish, if you need to distinguish it from other forms of Spanish). Second, this character is not Mexican, but Guatemalan, as is the actor who plays him. And finally, these two characters aren't buddies, but lovers.