Learn Portuguese (Portugal): A regra diz para nós vestirmos o colete.

Both are actually correct for reported directives! You can use dizer que + subjunctive (A regra diz que vistamos...) or dizer para + personal infinitive (A regra diz para vestirmos...). The para + personal infinitive structure is very common in everyday Portuguese because it allows you to express commands without needing to conjugate the trickier subjunctive forms.

Why do we need the personal infinitive vestirmos instead of the regular infinitive vestir?

We use it because the subject changes. The subject of the main verb (diz) is a regra (it), but the subject of the action of wearing is nós (we). When a preposition like para introduces a new action performed by a different subject, the personal infinitive is used to make it clear who is supposed to do that action.

Is it mandatory to include the pronoun nós before vestirmos?

No, it is optional. Because the ending of vestirmos already tells us the subject is "we", you can perfectly well say A regra diz para vestirmos o colete. Including nós here just adds a little extra emphasis or clarity.

The literal translation is "says for us to wear". Is this the normal way to translate "tells us to wear"?