I know but you use your Metamask as a sender and Kucoin account as a receiver.

Bad news is with Metamask wallet, you have its mnemonic seed then private key and you can import it to access to any chain supports by Metamask like ERC-20, BSC (Binance Smart Chain), and more.

With Kucoin account, you don't have its seed and private key, then your only chance is waiting for their support. You can not use your public key to import it to another chain. Kucoin owns that wallet private key, not you.