Magento Commerce Cloud is Magento-optimized PaaS (Platform-as-a-Service). It enables to fully automate continuous integration and continuous deployment of Magento eCommerce websites.
All the necessary installation steps for Blackfire are described in the Magento DevDocs.
The following video shows an example workflow when integrating GitHub, Magento Commerce Cloud, and Blackfire to automatically check the performance of your code at each commit.
Magento On Premise installations are all Magento installations that are not on Magento Commerce Cloud.
Blackfire works for Magento On Premise just like for any PHP application, and offers optional Magento-specific performance recommendations ("Magento Add-on").
Blackfire must be able to trigger PHP on the server where you are profiling (see how the Blackfire Stack works). To do so, you must make sure that caches are bypassed the Blackfire HTTP headers are preserved.