To run the FinalBuilder Task on VSO you require an agent capable of running FinalBuilder. This means creating a VM on azure to run a VSO agent and install FinalBuilder on.
Thankfully that are numerous articles online on how to setup an Azure VM to run a Team Foundation Build agent. The article Configure a Build vNext Agent from naked ALM Consulting is a great example of this.
Once the agent is running and registered with VSO you will need to Installing FinalBuilder so that it meets the "Demands" of the FinalBuilder task.