Walk slow.

It should be 'walk slowly', but yes, we use it at least in the US. We also have traffic signs advising us to 'drive slow'. I grit my teeth every time I see that.

Thank you.

My favorite sign of that type is: Slow, Children Playing. They leave out the comma.

Classic.

Using slow as an adverb may not be incorrect.

Dance instructors say "slow, slow, quick, quick, slow", don't they?

Sometimes in union disputes in Britain, employees, e.g. railway staff will stage a punctilious observance of all rules and regulations, including minor ones usually ignored, which they call a "work-to-rule". The media, especially unsympathetic newspapers, often say they are staging a "go slow".

Bryan A. Garner in “A Dictionary of Modern American Usage” says: “Though slowly is the more common adverb and is certainly correct, slow is often just as good in adverbial sense. … In deciding whether to use slow or slowly, let rhythm and euphony be your guides.”

Merriam-Webster's Collegiate Dictionary says: "Slow is almost always used with verbs that denote movement or action, and it regularly follows the verb it modifies <beans . . . are best cooked long and slow —Louise Prothro>. Slowly is used before the verb <a sense of outrage, which slowly changed to shame —Paul Horgan> and with participial adjectives <a slowly dawning awareness . . . of the problem —American Labor>. Slowly is used after verbs where slow might also be used <burn slow or slowly> and after verbs where slow would be unidiomatic <the leadership turned slowly toward bombing as a means of striking back —David Halberstam>"

I think that with traffic signs, lettering on the road surface, etc, rapidity of reading and (hopefully) comprehension and (even more hopefully) compliance favours the choice of the less frequent but still correct usage of "slow".

I do remember a regional TV news report that "SOLW" had been painted on the tarmac approaching a big road junction. The county authority said the painting team had "ignored the drawings supplied to them".

My teeth are nothing but nubs.

you can also "walk softly and carry a big stick"...