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I am not that familiar how the avatar in Virgin Airlines are presented.
However, if you have your own list of avatar and want to display them as an option in your form, then that is possible.
You can use the Image Radio button widget to set the avatar images as an option: Here's the link: http://widgets.jotform.com/widget/image_radio_buttons
Or you can also use the ddSlick Dropdown widget: http://widgets.jotform.com/widget/ddslick_dropdown.
To add a widget in your form, simply follow this guide: http://www.jotform.com/help/252-How-to-Add-a-Widget-to-your-Form
Let us know if you need more help on this.