No you don't have to know Flash. Certainly, begin comfortable with Flash timeline and drawing tools won't help you since they don't exist in Flex.
But if you are already comfortable with ActionScript, you'll have a head start.
The Flex in a Week tutorials are pretty good - although I found Day 5 to be very messy with some of the exercises having errors.
You can also try Lynda.com for similar lessons that take a different approach but will teah you essentially the same things. The earlier Lynda.com lessons give better information on how to work with the Flex UI.
So far I've not found any tutorials that cover the use of the debugger in detail, nor have I found any that include information on the most important thing about any development tool - excuse me while I shout.
C O M M E N T I N G Y O U R C O D E !
The best way to learn Flex is to go through the Flex Builder help sys page by page. I went through 3/5 of it twice, and it gives you an incredible grasp of the fundamentals.