Maybe a stupid question but I just don't get it.
I have a Set<Either<Failure, Success>> and want to output a Set<Success> with Arrow-kt. 
You can map the set like this for right:
val successes = originalSet.mapNotNull { it.orNull() }.toSet()
or if you want the lefts:
val failures = originalSet.mapNotNull { it.swap().orNull() }.toSet()
The final toSet() is optional if you want to keep it as a Set as mapNotNull is an extension function on Iterable and always returns a List
PS: No stupid questions :)
Update:
It can be done avoiding nullables:
val successes = originalSet
  .map { it.toOption() }
  .filter { it is Some }
  .toSet()
We could potentially add Iterable<Option<A>>.filterSome and Iterable<Either<A, B>.mapAsOptions functions. 
Update 2:
That last example returns a Set<Option<Success>>. If you want to unwrap the results without using null then one thing you can try is to fold the Set:
val successes = originalSet
  .fold(emptySet<Success>()) { acc, item -> 
    item.fold({ acc }, { acc + it })
  }
This last option (unintended pun) doesn't require the use of Option.