I can see no mistake in it. That said, I'd be keener on resorting to a bare infinitive preceded by "to" which would make your sentence look as follows:
"Learning to swim is not what I want to do during my holidays."
Not because the use of conjoint gerunds is improper but because it doesn't make the sentence sound pleasant. In the present case, the verb learn can coexist with either a gerund or a full infinitive, so go for a full infinitive !
(As an indicator, try and type "learning swimming" on the google bar and see what how many results you get. It can be misleading but most of the time truly reflects the usages, misuages and non-usages of a given phrase)
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