It seems there are carriage returns in your data.
Simply add the following to your stored procedure:
REPLACE(Address,CHAR(13)+CHAR(10),'')
+1
But still as you mentioned "SSIS Help with flat text file issues" suggests that you are using the SP written by someone else
OP mentioned it is a procedure that he wrote. One thing to note is that doing the update at the source with your stored procedure is more efficient especially if you are dealing with a great amount of rows as opposed to doing the change in the data flow.
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