"A kicker ability" includes the multikicker variant, which doesn't appear in Zendikar Rising. If you cast a spell with multikicker, the first ability will trigger only once, no matter how many times you kicked the spell.

You draw a card and discard a card while Coralhelm Chronicler's first ability is resolving. No player may take actions between those events, and nothing can happen.

If a card or token enters as a copy of a permanent, the new permanent isn't kicked, even if the original was.

The kicker ability doesn't let you pay a kicker cost more than once.

If you copy a kicked spell on the stack, the copy is also kicked. If the copied spell is a permanent spell, the token the copy of that spell becomes when it enters is also kicked.

If you put a permanent with a kicker ability onto the battlefield without casting it, you can't kick it.

If a spell's kicker cost was paid, the spell is "kicked."

To determine a spell's total cost, start with the mana cost (or an alternative cost if another card's effect allows you to pay one instead), add any cost increases (such as kicker), then apply any cost reductions. The spell's mana value remains unchanged, no matter what the total cost to cast it was.