What is the maximum email sending rate when using Amazon SES out of the sandbox?

You should be able to locate the sending rate on the SES console, on the dashboard. When I opted out of sandbox I received a quota of 14 emails per second, for my requested scenario, but yours might be different.

In any case you can request a quota increase by using the "Service Quotas" feature to better adapt to your requirements, you will need to explain why you are requesting the increase and they will get back to you with the revised quota, if applicable.