The game does not support cloud save yet, but the feature is planned for a future update. However, any purchased non-consumable items will be bound to your Google or Apple account, and logging into that same account on a new device will grant you access to those purchases even if game progress isn't transferred.
Skins bought with real money are considered to be non-consumable items, where buttons, skins bought with buttons and boosters are consumable and can not be transferred.