I've been reading up this morning, and all the documentation I can find claims that a CSV that looks like this will properly import:
"Issue Type","Summary","Epic Link","Epic Name"
"Epic","Test Epic 1",,"Epic Name 1"
"Story","Test Story 1","Epic Name 1",
"Story","Test Story 2","Epic Name 1",
"Story","Test Story 3","Epic Name 1",
But when that import is run, it turns out that Epic Name is not an applicable field for Epics.
Cannot set value for locked custom field 'Epic Name' in issue 'Everything to do with getting a user registered and logged into the site' because it is not applicable for issue type 'Epic'
As a result, there's no way to relate a task to its epic.
I've tried using the Issue Id + Parent Id combo that the task/sub-task relationship relies on, but those complain if you try to use an Epic and a Story, because Story is not a "Subtask" type.
I also tried exporting issues into CSV from Jira, to see how a properly-formatted CSV should look. That has a "parent" column which ties to the "Issue Id" column, but there is no ability to map to a Parent field in the CSV import.