I know nothing of CA law but I found this in the code:

Flashing lights are prohibited on vehicles except as otherwise permitted. http://www.dmv.ca.gov/pubs/vctop/d12/vc25250.htm

And the permitted uses http://www.dmv.ca.gov/pubs/vctop/d12/vc25251.htm don't include bicycle headlights (but do include motorcycles in daytime)

BUT, someone said earlier that California is a little weird in that bicycle doesn't necessarily mean "vehicle" in the Vehicle Code so this could be a gray area.