"Protected speech" refers to a limit on government action, that the government cannot arbitrarily restrict expression. Private agreements are outside of the domain of First Amendment protections, so an HOA can ban or not ban as it sees fit.
Whether or not a municipality prohibits some action does not change the status of the action as protected speech vs. something else. If there is no law against it, then the question doesn't arise. If there is discussion of banning the action, there is consider potential for discussion: would it be constitutional to outlaw the action?
"Speech" does not refer to identifiable words in a language, it refers to a "message", abstractly. I can imagine there being some expressive content associated with 20 Hz light flashing, so the question would be whether the governmental interest in prohibiting nuisances would be great enough to allow some reasonable limit on blinking lights. Noise ordinances are nearly universal (and constitutional), and definitely limit expressions. A complete ban on blinking lights would not be narrow enough to pass strict scrutiny, and I suspect a ban set at 2-40 Hz could (I'm pushing the lower limit on the frequency of seizure-inducing).