Flippy I think it's the exact same app as the Alcatel Go Flip V, so I'm talking from my experience on that phone. Overall, it's not the best app. It could be very laggy, you sometimes need to refresh a bunch of times to get it working, it clicks on links even without a browser (though it's bad at displaying them), all of your labels might not show up, when you're scrolling in an email, it just goes to the first link (you can fix this by clicking on the body with a mouse once), and the overall email experience is not the best, but it gets the job done. I haven't invested much time trying to find an alternative because I just need something that works.
As per the login, it supports Gmail, Outlook, Yahoo, AOL, and others that you can configure manually. You need a browser if you're configuring your email with the default options. I only have experience logging in with Gmail, and that's a piece of cake.