If you are using one of the forms that comes after the dummy data import you have to make sure that you have changed the Mail Settings and remove demo_mode from Additional Settings Tab in Contact From 7. 

It is worth noting that sending and receiving emails depends on both the server where your WordPress installation is hosted and the email configuration of the local computer where the emails are supposed to be received. Possibly difficulties here have not to do with the theme itself as we change nothing on the way that the CF7 function.

You can check some troubleshooting guides:

http://contactform7.com/setting-up-mail/

http://kb.cf7skins.com/contact-form-7-email-issues/

If you have configured properly the Contact Form 7 you could check in your spam folder maybe is there, otherwise it might be a problem with your mail server.

Another alternative and useful plugin is an SMTP plugin to set up like: Post SMTP  or WP Mail SMTP