You can get around this by creating a new column of type DT_DBDATE and using this new column to write to the CSV file.

First, add a new derived column transformation between your source and destination.

Next, add a new column to the derived column transformation. In the Expression field, use something similar to the following: (DT_DBDate)MyOriginalDateColumn. Replace MyOriginalDateColumn in this sample with the name of your date column from the source query. Use the <add as new column> selection to be sure this is a new column.

Finally, in your flat file destination component, use the new date field you just created in place of the original date field from the source.