So you want to use Cloudflare SSL certificates with AWS API Gateway?
First, 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 will ask you for a certificate chain. You can get that here.
Click Review and Import.
You are now ready to use it in the AWS API Gateway.