Do you want them to manipulate the items on the form or do you want them to actually edit the Sharepoint Lists? Insert, Delete, etc.
If it is just within the form you would need to build a list in the main data source.
So as they select items from the SP list it would copy them to the list in the form.
I would probably do this with a repeating table and use a button and then put an action on the button to copy the record.
Then another repeating table would list the items in the form list. A button there could be for removal.
Not sure how this behaves in a browser form but should be fine.