Can I use Database Engine Tuning Advisor for Azure?
No. The error message is correct - it does not support Azure SQL. There is no SQL 2016 for "Azure SQL", but there is SQL 2016 on an Azure VM, which is the same as any traditional SQL Server installation (more or less). 

That thread was confused, I assume, between SQL Server on an Azure VM and Azure SQL. 

Using the Azure Portal you should be able to check out index autotuning.