Is it a common pattern in having two AlwaysOn Availability Groups for DR and Reporting? We have a primary OLTP server in the cloud. 

We intend to have Synchronous Alwayson Availability Group for Disaster Recovery,
and another Availability Group AAG for Ad-hoc Query Reporting.
This way if our Primary Server goes down, there will not be contention between our Second DR server and Reporting queries. Reporting will be a third node. We will not require different schemas or indexes on the Reporting Server. Do you see any flaws with this design pattern or is it generally common practice?
This would be one AG with 3 replicas, not two separate AGs.

In general is fine, but probably overkill.  Normally if you have an FCI and an AG replica for DR you would use the DR node for reporting.  In a disaster you wouldn't have a separate reporting replica, but disasters are, you know, bad.

For Quorum, a cluster with a single FCI should normally use Node and Disk Majority (or Node and File Share if the databases are stored on SMB shares).  Neither of the other nodes should have a vote. 

See WSFC Quorum Modes and Voting Configuration (SQL Server)