Here's how I interpret it:
My fantasy is having two men at once.
This has a very obvious sexual meaning.
One cooking.
One cleaning.
This makes you reinterpret the earlier sentence with a non-sexual meaning:
My fantasy is having [one man cooking for me while another man cleans for me].
This subverts your expectations, which may be funny to you (depending on your sense of humor).
I think it retains some of the overtones of the original sentence, however.
ell.stackexchange.com/users/230/snailplane
Neither of the words "cooking" nor "cleaning" have any sexual connotation whatsoever.
That's the joke.
By attaching such mundane activities to a fantasy , one that starts with such an obvious sexual tone, it becomes a turn of phrase meant to make you laugh.
It's a PG-rated joke.
I'd like to add one small thing.
Even though it is becoming less so, cooking and cleaning are still considered tasks that fall to women.
So in this case, a woman fantasizing about two men performing those tasks is a play on gender-roles and her wish to escape them.
I'm a heterosexual woman, but I often joke that what I really need is a wife.
The joke in question has a similar play on traditional gender roles.
ell.stackexchange.com/users/4686/Jolenealaska
It's a joke.
When you read the first sentence -- "My fantasy is having two men" -- you immediately think that she's talking about sex.
Then when she says "one cooking, one cleaning", she is saying that it's not about sex at all, it's about housework.
That's why it's a joke.
She starts out making you think she's talking about sex, then pulls the rug out from under you when she makes it apparent that she's NOT talking about sex.
(I think this joke is originally from Rita Rudner.
Personally I thought it was pretty funny.)
ell.stackexchange.com/users/803/Jay
Jay is 100% correct.
The humor lies in the overturning of expectations in the set-up line from the word “having,” which, in English, has a clearly sexual connotation.
This joke works well in English because the language is compact — in this case, all the punch-line words are Anglo-Saxon, rather than Latinate, and therefore more efficient from a timing and syllabic perspective.
Think how awkward this would be in French, in which language you can’t just say “having two men,” without violating the grammatical rules of L’Académie Francaise: J'ai deux hommes.
L’un qui fait la cuisine et l’autre qui fait le ménage .
Somehow, this lacks the punch (by the way, French perfection is not guaranteed).
ell.stackexchange.com/users/4923/Red Howler
Despite how ruined I've become thanks to the internet, I don't think this one is a sexual joke, but a common joke that is not limited to English language only.
In my interpretation, the tweet describes a situation where a woman has two lovers who do some of her housework.
As a male, let me tell you that cooking a full course meal for even a small family and washing all the dishes afterwards takes a lot of time and is very exhausting.
You could swap the sexes and get a joke about how a man wishes he could have all his house work done by two women.
And in some countries this isn't a fantasy or even an uncommon scenario.
ell.stackexchange.com/users/2558/user1306322
I don't think that it's meant to be sexual in this instance - it's a fairly straightforward joke.
Some alternatively-minded people might read it as sexual, though: 'cleaning' is one word used to refer to a person giving oral to a female (can be male, but more often female) after she has had sex without a condom.
ell.stackexchange.com/users/4902/Macheleon
While just about any word can be given a tone of sexual innuendo in the right sentence,
e.g. I took the guy I met at the bar home with me and he really cleaned my clock!
the whole point of this joke is that the meaning is not sexual after an opening that implies something sexual will follow.
It's a common enough interpretation of gender stereotypes that men fantasize about sex and women fantasize about having a man to take his share of the domestic burdens.
ell.stackexchange.com/users/30533/arp
Just read a tweet,   My fantasy is having two men at once. One cooking. One cleaning.   Is it a word play in which 'cleaning' refers to a sexual intercourse or, actually, 'cleaning' is there intended having its literal meaning?
Should "cooking" and "cleaning" be taken literally in "...two men at once. One cooking. One cleaning."
ell.stackexchange.com
<word-meaning><phrase-meaning><jokes>
ell.stackexchange.com/questions/18538
ell.stackexchange.com/users/None/
It's a joke. By attaching such mundane activities to a  fantasy , one that starts with such an obvious sexual tone, it becomes a turn of phrase meant to make you laugh. Neither of the words "cooking" nor "cleaning" have any sexual connotation whatsoever. This is a joke. Neither of the words have sexual connotations.
This is a joke. Neither of the words have sexual connotations.