Unfortunately, MetaMask does not support the option to export your key in JSON format. The following guide will show you a workaround on how to do it.
Go on the MetaMask browser extension and click the three-dotted settings icon.
Click on ‘Export Private Key’, confirm with your password and ‘Export as file’. You will download your private key as a CSV file.
Go on wallet.parity.io. You will have to accept all the terms and conditions and create a Ethereum account. The account you are creating has no importance to this process, but you will have to do it in order to proceed. Once you have created an account, go on the ‘ACCOUNTS’ tab and click ‘+ ACCOUNT’. Select ‘PRIVATE KEY’.
On the next page you have to enter your raw private key from MetaMask (add the prefix ‘0x’). Give the account a name and select a strong password. Finally import the account.
Click on the just imported account and select the ‘EXPORT’ option.
Type in the password you just specified. Parity will download the JSON file.
I am no longer working in the cryptocurrency space and no longer have any interest being involved with it. I would get in contact with someone with more understanding. Sorry I can’t help more!