"despite never having learned" vs "despite never learning"

Both are acceptable, but "despite never having learned" sounds like a reference to the past, whereas, "despite never learning," sounds more like a present condition. The meaning should be clear from the context, though.

The "having / not having" is the gerund form of "have learned" or "had learned." (Rule: Preposition + gerund; here, "despite" is a preposition.)

I've noticed that in constructions like these, careful writers may sometimes add the "having" to emphasize the time frame, but may sometimes omit "having" to be concise and less wordy. I haven't confirmed this with corpora databases, but this is my observation. Similarly, there are many instances when the past perfect, had + pp, is optional and simple past can be used.

Either potentially works.

First, I would like to point out the first example is, to most people at least, past continuous tense due to context, not the present continuous that it appears to be. Conditional clauses in English that start with ’despite’, and especially those with negation of the verb in the clause, tend to get really weird when dealing with continuous tenses, as they are almost always written to explicitly be past continuous or present continuous and you have to infer from context which is meant. In this case, it’s past continuous because of the use of never (’never’ can never be used as part of a purely present tense verb phrase, the associated verb must always be in a past or future tense).

As far as the meaning, either of them may loosely imply any of the following depending on exact dialect, who you’re saying it to, and even the way you say it:

• You were taught, but did not retain the knowledge or skills (this would be more strongly implied if you used ‘never really’ or ‘never truly’ than it is when just using ‘never’).
• You had the opportunity to learn, but chose not to.
• You had the opportunity to learn, but something else prevented you from learning it.
• You never had the opportunity to learn.

Notably, they may not actually imply the same thing, or they may imply the exact same thing, and that also depends on exact dialect, who you’re speaking to, and how you say it.

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As a slight aside, you could also write the second form as ‘I’m good at this, despite having never learned it.’. This is actually how I would personally phrase it (though that’s probably just as much influence from studying other Germanic languages where the negation must go between the accessory phrase and the verb). This generally works no matter what the tense of the verb being modified, and even (mostly) independent of the adverbs being used, though which form (‘adverbs accessory verb’ or ‘accessory adverbs verb’) is more preferred depends both on dialect and how long the full set of adverbs is.

The second isn't really preferred, but it's what a mid-class native speaker would say. "Never having verbed" is a common, fun, often shorter replacement for "never done that".

You might say "Never having owned a snake, I don't see how they're fun". Or "You would think that, never having been pregnant yourself". Or "I did OK, for never having read the manual".

I'd add that, regarding your example, "learning" has a broad meaning. If you're good at something, that means you did learn it. It's more common to say "never having been taught" or something else specific that many people use to learn it.

I'm good at this, despite never learning it.

According to me, the above sentence sounds like you had several many opportunities that came your way, but you neglected them, intentionally or absentmindedly.

I'm good at this, despite never having learned it.

This sentence shows your lack of opportunity. You almost never got a shot at learning those things required for the skill to be developed.