Can I 3way cfls in series?
 

I have this diagram I'm following, but the problem is that the lights flicker and if I remove one of them the others go out.

That is parallel wiring. ALL AC building wiring is parallel, regardless of the physical orientation of the lights and switches.
Things like alarm systems are wired in series.

You obviously wired them electrically in series, which is NOT good.

I agree with speedy, if they were in parallel they wouldn't go out when you removed one.

can you take some pictures of your setup? maybe the backs of the lights?

Are you telling him that's the only reason not to wire the cans in series? I can understand receptacles, but cans?

It looks to me that the diagram is accurate. And you've wired it incorrectly

You probably need another wire ran between the four lights .. Or depending on what's easier access
Run a traveler directly between we the switches. Hard to tell since we don't know what you've done.

If we are to assume you are an electrician by your name, do you know the difference between series and parallel???

The drawing is correct. If removing one makes the others go out then you did not wire it like the drawing.

Thanks for the replies everyone.

This is an old house and I'm using existing wiring, the diagram was roughed out as a plan of action.

Everything is working now. I had mixed up the black and white coming pff the last switch. Using a miltimeter I found which wire to use, the white was hot and the black wad neutral (old existing wire).

Thanks for the update.:)