When the ability resolves, Flickering Spirit is exiled, then immediately returned to the battlefield. It returns as a "new" creature. Any counters, Auras, and so on are removed. Any spells or abilities targeting Flickering Spirit no longer target it.

If Flickering Spirit's ability is activated, any "as this enters" choices for it are made by its owner, not its previous controller.

If a token copy of Flickering Spirit uses its activated ability, the token will not return to the battlefield, because of the rule that says tokens that leave the battlefield can't return.