Two questions.

First, why are you copying the records with a different sequence no (really just curious about the business requirement)

Second, why does it have to be done in SSIS? A simple T-SQL statement can do it just as easily. The only thing that bothers me is that you are doubling the number of records in the table, and that could explode you t-log on the table.

There are ways to manage this possibility, but it means knowing more about the data and the table in particular (unique or primary keys to be exact).