If Kayn uses Ride the Wind to move to an opposing battlefield and becomes ready, but cannot conquer the battlefield and is automatically sent back to base (because it can't take damage after moving twice), does Kayn retain its ready status when recalled to base?

Yes, Kayn retains its Ready status when recalled to base. Recalls do not affect the state of the Permanent being recalled. The rule states: 'Unless otherwise stated by the source of the Recall, Damage, Exhausted Status, Buffed Status, and applied Layer alterations will all remain unaffected by a Recall.' Since the recall is a corrective action due to Kayn being unable to conquer the battlefield (it cannot take damage after moving twice and therefore cannot be killed), and the recall doesn't specify otherwise, Kayn's Ready status from Ride the Wind is preserved. Kayn will be in base in a Ready state, available to act on the next turn or immediately if other actions are available.