SQL Server 2016 AlwaysOn DBCC CHECKDB on async replica
I can say that the error message you are getting is because of a bug in SQL Server 2016. Microsoft knows about it and has fixed it in CU3 for SQL Server 2016 RTM.
Note: The user error is reported but the CHECKDB should continue as is.
See FIX: Error 976 occurs when you run the DBCC CHECKDB command on an unreadable secondary replica of SQL Server 2016 Availability Group
Workaround
You can take snapshot of the databases and can run checkdb on it. In this case it would not fail.Database snapshot is enterprise feature I am sure you are not using basic availability group