We don’t have any first-hand experience install FluidFlow in the Azure environment, but there is no reason why it would not work.
The FluidFlow license is locked to the serial no of the hard disk of the server it is installed on. From our understanding of Azure (based largely on this: https://azure.microsoft.com/en-gb/blog/accessing-and-using-azure-vm-unique-id/), as long as the client enables this feature, and the VM is not allocated/deallocated on demand, it should be possible to migrate FluidFlow to Azure.
For instructions on transferring to another server: https://knowledge.fluidflowinfo.com/knowledge/fluidflow-transferring-to-another-server