Books serve two basic uses: How-To, and Reference, generally these functions overlap.
References are essential. Flash is complex. Keeping all the details of the program in your head is a daunting task, which will only develop with practice. Using a book for How-To learning helps you gain that practice, and has the advantage of being self-paced. Reference books aid your memory by providing extensive explanations of every aspect (there is also a built in reference system in Flash; USE IT!).
One of the advantages of a book over a website is the editorial function involved in publishing for print. Often, the authors online express their opinions as if they were facts, or simply make mistakes. Books are not immune to this, but they are generally subject to stricter review policies. On the other hand, web sites can be updated with the latest developments. Conclusion: use both.
PeachPit Press, QuickStart Guides
Macromedia Flash MX for Windows and Macintosh: Visual QuickStart Guide
Flash 5 for Windows and Macintosh: Visual QuickStart Guide
Flash 5 Advanced for Windows and Macintosh: Visual QuickPro Guide
Flash MX Bible
Flash 5 Bible
ActionScript: The Definitive Guide
Colin Moock (Sebastapol, CA: O'Reilly & Associates, 2002)
goto: moock.org >> codedepot for associated online resources
Also look for:
ActionScript for Flash MX: Pocket Reference
Colin Moock (Sebastapol, CA: O'Reilly & Associates, 2003)
Macromedia Flash MX Designer's ActionScript Reference
Sham Bhangal, et al. (Birmingham, UK: friends of Ed, 2002)
goto: friends of ED site and see even more Flash MX books