Sounds like you have created a unique constraint or unique index on the table that didn’t exist on the Oracle database, or you are trying to insert the records a second time.
It could also be that the Oracle table was case sensitive, while the SQL Server defaults to case insensitive. If this is the case and you have the value “Test” and try to insert the value “TEST” you’ll get the duplicate key error. This can be corrected by changing the collation of the column, table or database to a case sensitive collation.
If there is no matching constraint on the Oracle database, simply remove the constraint.