Is it legal to require "flexing" of an employee's schedule to avoid having to pay overtime?

If by flexing you mean changing schedules at the last minute and sending employees home to avoid having them incur overtime i.e. not working over 8 hours a day or 40 hours in a week, yes, it is 100% legal in all 50 states. Nowhere does the law give you the inherent right to work overtime.

The above presumes that no legally binding contract or CBA expressly says otherwise.

Still legal. There is nothing in the law that prohibits them from changing people's schedules around. For any reason.

Same caveat.

It's not that there is a law that gives the employer permission to change schedules; it is that there is not a law prohibiting it.

You are required to choose schedules that far ahead because that's what the employer wants you to do. There is no law that requires that, either.

How your hours get scheduled, when or even if you choose your shifts, and when and under what circumstances they can be changed, are all up to the employer. There are no laws whatsoever that directly affect scheduling.

Unless I'm missing something here, like the OP get a 4 hour lunch break, there's overtime involved. California has regulations requiring 1.5x pay for any hours worked over 8 in a day. A shift of 6am to 6pm with the required meal and rest periods would wind up with 8 hours of straight time and 3 hours of overtime.

Good point. I didn't stop to figure out the shifts involved since the question was solely about the legality of changing schedules.

OP, since you are in CA (this would NOT be the case in most states) if you are working over 8 hours a day you are entitled to overtime. This is a completely separate question than the schedule changing one.

http://www.dir.ca.gov/dlse/FAQ_Overtime.htm

OT must be paid for any work over 8 hours in a day OR 40 in a week.

If you are working in a 911 center - are you unionized? Is there a collective bargaining agreement in place?

This could affect your OT claims.

Just a thought, but if we are talking about a governmental employer, then my understanding is that we not only have the possibility of comp time from federal law, but that the "normal" CA daily overtime rules also change. Not having worked for a governmental employer, I have never bothered running down the details of that, but it something that I have heard before. Consider this to be a "soft" answer.

First responders such as police and fire have different overtime rules, but that's not you.

Having managed the payroll operation for a large city, I can help on the federal level, but that city wasn't in California.