Can a 2008 SSIS package Connect to a Newer SQL Instance?
SSIS can connect to many different servers based on the connection type used in the SSIS package. Since even SQL Server 2016 SSIS still uses Native Client 11 (and has since 2012), you should not have any issues connecting from SSIS 2008 R2 to SQL Server 2016. SQL Server 2008 R2 uses Native Client 10 or 10.1 but has no issues connecting to SQL Server 2016 either.

In the connection manager in SSIS, you choose the way to connect to SQL Server. It could be ODBC, OLE DB, or any number of connections types. I say this to say SSIS itself does not care what version of SQL Server you are connecting to but the task you use will determine the connection type. I would assume you are using OLE DB and as such you may choose the provider in the connection string.