The issue is likely due to the SSIS server (or it's service account) not having permission on the linked Oracle server, especially if SSIS is on a separate server to the SQL Server machine (or running from a different account). You may need to enable access either in the settings for the linked server on the SQL Server machine, or more probably on the Oracle machine.

Rather than using the linked server, why not create an Oracle connector in SSIS and connect to it directly? It will be much quicker.