Date picker not working in mobile device

Contact Form 7 has some Datepicker support via the new HTML5 date input type (see https://contactform7.com/date-field/) but this is currently only supported on some browsers – see https://www.wufoo.com/html5/types/4-date.html

You have little chance of this working on various mobile platforms IMHO. You would quite possibly need to write a device specifc mobile app to get effective Datepicker functionality.