Before I start, I want to unpick some assumptions that appear in the question, that are common in nature-versus-nurture questions.
When you ask "is there any proof that humor is genetics and not something you can learn?" you are introducing two false dichotomies.
The firstly is that it suggests that an attribute is either 100% genetics or 0% genetics. That ignores the common option that genetics may account for some, but not all, of the variability.
Secondly, it ignores other effects - such environmental factors, and personal factors unrelated to training.
Epigenetics are another confusing factor that undermines the either-or nature.
A good way to evaluate whether an attribute has a strong genetic component is to use twin studies. If there is a strong genetic component, we would expect that identical twins would have a more similar expression of the attribute than fraternal twins.
Using twins means that most of the confounding factors, such as upbringing, education and socioeconomic factors are close to identical.
This study evaluated 127 pairs of female twins at their response to cartoons.
They found that sisters tended to have correlated responses, but identical twin sisters did not have higher correlations.
This pattern of correlations suggests that shared environment rather then genetic effects contributes to cartoon appreciation. Multivariate model-fitting confirmed that these data were best explained by a model that allowed for the contribution of the shared environment and random environmental factors, but not genetic effects.
Assuming that evaluation of cartoons has a reasonably strong correlation to the ability to produce comedy, it seems that there is not a strong genetic component.
However, shared environment has an effect. This does not prove or disprove that training in comedy can help. It only disproves that one is born funny genetically.