So you want to use Cloudflare SSL certificates with AWS API Gateway? Its easy! First, you need to create an origin certificate in Cloudflare’s and then import it into the AWS Certificate Manager.
Cloudflare -> SSL/TLS-> Origin Certificate -> Create Certificate
Open the AWS Certificate Manager and provide it with your certificate body and private key. The certificate manager is going to ask you for a certificate chain. You can get that certificate here.
Click Review and Import. You are now ready to use it in the AWS API Gateway.