I hear this a lot, and there is a lot of confusion out about this.
First, to engg_fahd's comment: Flex is Flash. Flex is a flexible language which can integrate with many other technologies (typically ActionScript 3). It is packaged into a SWF, which means it is Flash.
Back to HTML 5 vs. Flash.
HTML 5 is a lot better at doing many things. Like Mike said, some things that Flash is commonly used for will be replaced with HTML 5 (namely video and audio). Also, Adobe is discontinuing their mobile browser Flash plugin since many people that tailor sites appropriately for that are just using HTML 5 (since phones now have very good HTML 5 support). However, Adobe is no discontinuing Flash on phones altogether... they are just switching to focus on Flash as apps (via AIR), which makes more sense.
Flash isn't going anywhere for a long time. It will take -at least- another 5 years before you can use HTML 5 with impunity. In the mean time, Flash will have much better overall availability and is more universally acceptable.