I'm going to implement some voice chat on my website (the website is as usual on HTML/CSS/JS/AJAX) and I wonder what's the fastest way to do it via flash (I mean that there are many different technologies RTMFP, VoIP, VoiceXML, ... what to choose?)
Could you also suggest some good solution for implementing server-side part of that stuff?
VoIP isn't really a "technology", it's just the end result. Any and all voice chat over the Internet will implement VoIP in some form or other.
If I were doing it, I'd probably use XMPP for presence management (telling/finding who's online, managing lists and groups, etc.), SIP for call setup (deciding on a codec based on what both sides support), and RTP for transport (getting encoded data from one end to the other). Chances are pretty good that you'll also need (or at least want) TURN and STUN to make it work from behind NAT routers.
If memory serves, Flash has its own media transport protocol, but I believe it's oriented primarily toward streaming video from Adobe's server product(s?).