Not 100% sure, but I thinks this is how you should do it:

1. Take an Execute SQL Task and execute your stored procedure there with the following code:

EXEC my_stored_procedure my_par1 mypar2 ... ;

GO

2. In the General Tab, set Result Set to Full Result Set (I hope this can be done with stored procedures)

3. In the Result Set tab, write the results to a variable of type object.

4. Create a data flow task and add a script component that acts as a source. Read the object variable and write it to the output buffers. Then write it to a flat file destination.