1. Open your form.

2. Add list component to your form.

3. Choose 'Contact' as a source object.

4. Provide title and unique list name, add columns.

5. Save a form.

6. Create an Action.

See details in How to create Action article.

7. Choose 'Account' as a context object type for your action.

8. Choose 'Action' type and 'Field Update' action type.

9. Choose 'Contact' object.

10. Click 'Add Field' button, choose 'Level' field and set it to 'Primary'.

11. Click 'Add Condition' button, define condition so that only contacts selected by user will be updated to Primary. Use {$Environment} object to get the list checkboxes data: {$Environment.vf_contact_list}.

12. Save your changes.

13. Add new custom button to your form.

14. Tie it up to the action.

See Actions for details.

15. Save the form.

16. Run the form (add Account id to the form URL).

17. Choose several contacts in the list and click the button - as a result of  Action execution those contacts level will be updated to 'Primary'.