Title says it all, what is the most recent version of Sql Server native client that is compatible with Sql Server 2008 R2
Microsoft SQL Server Native Client 11.0 is the latest and is backward compatible with 2008 and 2008R2 (as of July 9 2019, both windows and sql server 2008 and 2008r2 are fully unsupported).
BOL warns you :
The SQL Server Native Client (SQLNCLI) remains deprecated and it is not recommended to use it for new development work. Instead, use the new Microsoft OLE DB Driver for SQL Server (MSOLEDBSQL) which will be updated with the most recent server features.
SQL Server 2008 R2 is out of support, but AFAIK every existing SQL Server client library, including all SNAC and ODBC drivers should work fine with that version.
I believe, there is no version beyond
SQL Server native client 11.0 which you can use for SQL Server 2008