How do I create a multi-part field (similar to phone number)

You may consider using the following widgets:

https://widgets.jotform.com/widget/infinite_list

https://widgets.jotform.com/widget/matrix_dynamique

https://widgets.jotform.com/widget/configurable_list

https://widgets.jotform.com/widget/configurable_list

To add a widget, please follow our steps here: https://www.jotform.com/help/252-How-to-Add-a-Widget-to-your-Form.