Flash player works fine, the plugin is self updated by Chrome OS and works with pretty much any website using flash, never had an issue with it. You should be fine. Prime and Netflix work fine on this model too, without apps.
I have this Chromebook and I just went onto CBS.com and tried to play an episode of Hawaii Five-O. It works, went full-screen and in HD, has closed captions, the whole nine yards. Right now it is paused as I type this review on another tab, right now I have three tabs with video streaming from Netflix, Hulu, and now CBS.com with Hawaii Five-O, and all are running with no problems, all while I type here on this page. There shouldn't be any problems, I have also watched episodes on other sites like The Walking Dead on AMC.com and Spartacus on STARZ.com with no problems as well.