Translation:We would often get books from our parents.
"We often got books from our parents" is also perfectly fine and is an accepted translation.
I think it's because of the aspect difference between “dostat” and “dostávat.” Here “dostváli” means that we kept getting books, or that we got books over and over again. DL expresses that by “would.”
I am not sure of the difference to “we often got,” or whether such a sentence is even grammatical in English.
Does "We were often getting books from our parents" not work for any particular reason? Not accepted as of this writing, I'd specifically used that wording to capture dostávat being imperfective.
In a sentence like this, "parents" is usually used with a possessive in English, but Czech allows the possessive to be understood rather than explicit.
So how can you tell if it's implied possessive or not? I interpreted the sentence in the context of 'a school asked parents to donate books'. The headmaster could say 'We would often get books from parents'. That would be exactly the same in Czech, right?
I am by no means an expert in Czech, but... I think there is a Czech convention that the possessive need not be specified with family relationships and body parts, and that personal "ownership" is assumed when a possessive is not used.
So my thought would be that, in the sentence you asked about, an explicit possessive might be required, to indicate that it's the students' parents to whom the headmaster is referring.
But an authoritative answer from one of the CZ natives on the team would be great, in case I'm totally wrong!