Is walking while a Don't Walk sign flashes against the law?

It’s not merely advisory. It has a real legal authority which can result in your getting a ticket - and that would be for people who left the footpath after it has started flashing*. Essentially, it has a very similar meaning to a yellow light for cars - do not enter the intersection unless it is too late for you not to. I suppose it could also be advisory in the sense of “oh shit, I’m walking too slowly, I’d better hurry up”, but I know I don’t pay attention to that light after I’ve stepped off the footpath, and I suspect most other able-bodied folk don’t either.

*In Sydney, there used to be small enamel signs explicitly stating this:

“WALK - you may cross the road
Flashing DON’T WALK - you may not start crossing the road, but may complete your crossing if already doing so.
Solid DON’T WALK - you may not cross the road.”

These signs seem to have disappeared, but they were everywhere when I was a kid.

It means you can finish crossing if you’ve already started, but you shouldn’t leave the curb:

What does the flashing DON’T WALK signal mean?

Illegal to start crossing once “don’t walk” sign starts flashing

“WALK…OR DON’T WALK? THOSE SIGNS ARE SO CONFUSING!” (pdf)

WHAT DO THE INDICATIONS MEAN?

http://www.dot.state.co.us/Traffic_Manuals_Guidelines/Informational_Brochures/Pedestrian_Signals_Brochure.pdf