Does Azure SQL Data Sync support MySQL or SQLExpress?
Azure SQL Data Sync does not support MySQL for synchronization but it does support SQL Server Express as you can read here. 

One of the troubleshooting steps is to exit local sync agent, then open the services.msc applet in Control Panel, make sure SQL Data Sync service is started, if the service is started please restart the service. If the service cannot start change the service account to a local Administrator of the computer. Reopen the local sync agent.

Try also to disable any security software (Avast, Windows Firewall). Start SQL Server Browser Service on the computer.

Another possible reason, the agent key that you have entered is invalid. The agent key being submitted is not the most recent; you may have regenerated a newer key on Azure Sync portal. Try regenerating on Azure portal and resubmitting.