If a token is exiled and then returned to the battlefield by a blink effect, does it still exist?

Tokens are not cards, and they follow a special rule: whenever a token leaves the battlefield, it ceases to exist the next time state-based actions are checked (CR 704.5d). This applies to any zone the token moves to — the graveyard, the hand, and crucially, exile.

A 'blink' effect works by exiling a permanent and then returning it to the battlefield. For a normal card, the object sits in exile briefly and the return effect finds it there. For a token, however, the token ceases to exist as soon as state-based actions are checked after it enters exile (CR 110.5g). There is no longer any object in exile to return, so the second part of the blink effect simply has no target/object to act on and fails to do anything.

This is true regardless of the blink effect used. Whether it says 'return it to the battlefield' or uses a delayed triggered ability, the token is already gone by the time that return would happen.

Concrete example: You control a 1/1 Soldier token and cast Flicker (exile target creature, then return it to the battlefield under your control). The token is exiled, state-based actions are checked, and the token ceases to exist. When Flicker's return effect tries to put it back, there is nothing in exile to return. The token is simply gone.

Relevant rules: CR 110.5g (tokens leaving the battlefield cease to exist), CR 704.5d (state-based action removing tokens from zones other than the battlefield), and CR 400.7 (objects changing zones are treated as new objects, though tokens never survive to matter here).