My wife has new Kindle fire hd
the email address is Hotmail. connection Wi-Fi.

I noticed checking her emails clicking the mail envelope logo you go straight to inbox listing her messages (two) how do you actually log out or isn't it necessary using Wi-Fi connection?.
Sorry if I've missed something
On my pc, as you know, you can logout and have to enter email address and password to get back in but can't see logout or exit on the Kindle.
Many thanks

Charlie, February 2014

I don't think that the fact that she connect over wi-fi have anything to do.
The more probable cause would be how the Kindle actualy works. It probably save the connection credentials, connect automaticaly as needed and disconnect when the e-mail app is closed.

Electro, February 2014