What you want to accomplish, is not very easy but not too hard also.
1. display the categories in a checkbox format or a multiple select list. Capture the Post value for categories as array. This is done in libs/templates/front-end-submission.php
2. In user-dashboard-add.php – you need to work with the current wp_set_object_terms to add all the categories. wp_set_object_terms accept array so should be pretty straight forward assuming you are sending the POST values correctly.