Profile Tab with CF7 form inside
You could integrate the Contact Form 7 (CF7) contact form with the Ultimate Member profile tab and display a contact form in the user's profile page.
Contact Form 7 plugin installation
Contact profile tab
So when you will have the ready-to-use your contact form please paste the form's shortcode to the profile tab content.
You may see this profile tab and a contact form at it. By default, all data will be sent to the profile's owner email.