Android: If you still need Flash support on your phone, Now Browser is a speedy web browser for Android that offers it. It features a clean design that's at home in KitKat and gesture support. It's not as feature-packed as other browsers, but it's fast, lightweight and gets the job done.
Now Browser's main claim to fame is that it's fast and flexible, and that support for Flash video and elements on a page is one tap away in the app's settings. You'll still need to find and install Adobe Flash for Android, but once it's installed, you can turn it on and off at will in Now Browser's settings. The browser itself is clean enough, and definitely fast -- you can swipe left or right to navigate pages, and the interface is simple.