Is it permissible for an intellectually disabled person, 22 years of age, to receive zakat funds, even if his father is well-off?

It is not permissible for your son to take from the Zakat money, because if he has wealth, it is incumbent upon you to spend on him from it. And if he does not have wealth, then his maintenance is obligatory upon you as long as you are able to provide it. Therefore, a person who is wealthy, either through his own money, or earnings, or through maintenance provided by someone upon whom his support is obligatory, is not permitted to be given from the Zakat.