You choose whether to kick a spell as you cast it, and you pay that much along with the spell's mana cost at the same time. Kicking a spell is always optional.

Kicker costs don't change a spell's mana cost or mana value.

You can pay any particular kicker cost only once. You can't pay it multiple times to get multiples of either triggered ability.

If Thornscape Battlemage is put onto the battlefield as the result of a spell or ability, there's no opportunity to kick it.

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

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

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.

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.

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