You only use the continuous tense if you are doing something right now or in the future, but not when referring to something you do on a regular basis. So you can say 'We are going to the park now/tomorrow/on Friday', but you use the present tense for the repeated action, 'We go to the park on Fridays'
That's not a future perfect (that would be "We will have gone"), but just the "going to" future.
There are a couple of arguments against it, most straightforwardly that it isn't called for in the Spanish sentence. The Spanish sentence only has one verb, vamos, and it means "we are going" or "we go". There's no additional "go" there; that would look like:
- Vamos a ir al parque los viernes. - We're going to go to the park on Fridays.
Also the situation is different. The original sentence sounds like we already go to the park regularly, a habitual present, so to say. Your sentence makes it into a plan for the future.
Mickey, the hints work like a dictionary - they show different translations of a specific word, but not every translation applies to every circumstance. Vamos can be translated as "should" when it's together with another verb, but that's not the case here.
- Vamos a ponernos los zapatos. - Let's put on shoes. / We should put on shoes.
It is wrong because you are only talking about one Friday and Duo is talking about multiple Fridays.
(Nosotros) Vamos al parque el viernes = We are going to the park on Friday.
Please note that the word for Friday 'viernes' has an 's' on the end regardless of being singular or plural. This is true for Monday (lunes), Tuesday (martes), Wednesday (miércoles), Thursday (jueves), and Friday (viernes). But not for Saturday (sábado) and Sunday (domingo). For them you would add an 's' for the plural.