After defused from Goku, in the Buu arc, Vegeta remembers how they badly beated Buu. If Vegeta has memories of the times being fused with Goku, why doesnt he learn his techniques such as the teletransportation, Genki Dama and Kaioken?
There doesn't seem to be a lot of information regarding this, but we have at the least this premise about the Potara Fusion technique: At the end of the time limit, the two fused together will be returned to their original selves, so long as neither of those fused was a Kai. We have this as a premise because Goku and Vegeta seem to retain their selves and unique personalities even after the fusion ends.
Now, what does it mean for one to return to being their original self? For Goku and Vegeta to be themselves, their memories and personality have to be put back to the way they were before the fusion. If Vegeta now has some of Goku's memories, then he isn't completely himself anymore. In this regard, it seems that there are no lapses: we don't see Vegeta act like Goku, or vice-versa, and they don't complain about retaining any memories. They both retain memories of what happened while fused, because they both experienced this. So if Goku or Vegeta retained one of the other's techniques, then they would have each other's memories, and the fusion would not have been completely nullified.
This would seem to be the case, but consider this: in humans, there are two kinds of memory: explicit and implicit, and these are further divided into subcategories. And based on studies, it seems these two memory systems might be separate. Goku and Vegeta's memories of their past experiences would be stored in their episodic memory, a type of explicit memory. Therefore, for them to remain intact, the most important type of memory would be explicit. Now, marital arts techniques would be retained in muscle memory, a type of procedural memory, which is a type of implicit memory. I suspect it would even be the case with techniques like the Kamehameha that they are stored, at least partially, in muscle memory, because they are gained through training and practice.
Since implicit memory and explicit memory are separate systems, let us entertain the notion that after fusion ends, Goku and Vegeta retain each other's explicit memory. In this case, it might be the case that they learn each other's martial arts techniques. Even supposing this is the case, this still will likely not be enough for Vegeta to use Goku's techniques. The reason is thus: Vegeta still lacks Goku's explicit knowledge of the techniques. There are two basic type of explicit memory: semantic, which deals with factual information and episodic, which deals with recollection of every day events. Both types are important.
To understand why, let's look at the Kaio-ken technique, and imagine Vegeta trying to use it. King Kai sat Goku down and explained everything he needed to know about this technique. There may be nuances about how to use your energy and things one needs to keep in mind when using it. These facts would be semantic memory. When it comes to wielding energy, these facts could be essential when it comes to wielding energy (we can't know for sure, because the mechanics of energy techniques are not well-defined in Dragon Ball). Another important factor would be the actual memories of using the technique from episodic memory. As for why this is important, we again return to the Kaio-ken. Goku must have clear memories of being in extreme pain after overusing this technique. Even more so than King Kai's warning, these memories will tell him, "Hey, don't use Kaio-ken x 100, because it'll really hurt afterwards!" But if Vegeta doesn't have Goku's implicit memory, he won't retain this either after fusion, so he won't have any sort of understanding of the technique or its drawbacks.
In conclusion, we suppose that it is a certainty that explicit memory of one's counterpart is not retained after fusion. We concede that it may be possible implicit memory is retained. But even in the event that implicit memory of one's counterpart is retained, it likely would not be enough to learn the other's techniques, because they would lack a full understanding of the techniques.
I got all of this from skimming through memory category pages of Wikipedia, so my knowledge on the subject is far from complete.