No, CloudFlare only offers that kind of customisation on Enterprise plans.
- CloudFlare will time out if it fails to establish a HTTP handshake after 15 seconds.
- CloudFlare will also wait 100 seconds for a HTTP response from your server before you will see a 524 timeout error.
- Other than this there can be timeouts on your origin web server.
It sounds like you need Inter-Process Communication. HTTP should not be used a mechanism for performing blocking tasks without sending responses, these kind of activities should instead be abstracted away to a non-HTTP service on the server. By using RabbitMQ (or any other MQ) you can then pass messages from the HTTP element of your server over to the processing service on your webserver.
