You probably won't have much luck without an idea to start with. Naturally, it's something other interested authors can expand upon, but you need an initial premise of some type to attract people who find the idea interesting.
And there's this, for once you get the ball rolling:
There's a lot of good information in that guide. Red's certainly done enough chain stories to know what she's talking about. I can only emphasize what she wrote by adding the following:
1) Take the time to learn who your collaborators are. Check out their posted stories. You may find that your writing styles differ. That can be a good thing, but sometimes, it's not. Also, email and/or chat with them. Learn their personalities, their ideas. Brainstorm together. Make sure everyone has the same idea about the chain.
2) Make sure everyone who comes on board for the chain is genuinely interested and willing to put in the time and effort. Follow Red's advice on keeping a time table. I've worked in chains that turned out beautifully; unfortunately, I've also been part of chains the fizzled out after the first posting.
3) Keep in mind that many writers have egos, and their own agendas. Sometimes, these egos will clash. If you're lucky, you will gather a group of writers who are humble and understanding enough to listen to one another and share ideas. But this may not be the case. Be prepared for the possibility that one or more of your collaborators may be disruptive, and be able to deal with that.
4) Lastly, if you start a chain -- in other words, the basic idea is yours, the premise is yours, the theme is yours -- you are in control. In her how-to, Red mentions deciding how and when to be firm on your ideas. You may find that some participants won't like your ideas; it will be up to you to either compromise, or put your foot down (to the point where someone may leave the chain).
All in all, chain stories can be very rewarding. You gain a groupthink sense of accomplishment once it has panned out and the stories are posted. However, being part of a chain WILL be frustrating. There will be time-management issues. Participants will have sudden emergencies, conflicting schedules, sudden cases of writer's block, etc. If you're in a chain, you need to be patient and understanding.
I hope this all helps. Writing a chain story can be a lot of fun. Just be upfront about what you want.