Is possible to run swing migration from SQL SERVER 2008 R2 to 2019 with Log Shipping?
Yes, It's possible.
You can migrate databases from older versions like SQL Server 2008 R2 to SQL Server 2019.
Check answer from here. Migrate to SQL Server 2019
Log shipping: Log shipping is supported if primary is running SQL Server 2008 SP3 or later, or SQL Server 2008 R2 SP2 or later, and secondary is running SQL Server 2019.
Warning: If an automatic or manual failover happens and the SQL Server 2019 instance becomes primary, SQL Server 2008 or SQL Server 2008 R2 instance becomes secondary and cannot receive changes from primary.