“escaped prison” or “escaped from prison”?

I'd say both are correct, although my preference in this case would be "escaped from prison".
Escape without from is appropriate with words like censure, notice, punishment, comment.
It just doesn't sound right when used in that fashion with words like prison, gaol, confinement.
The "escaped prison" is, I suspect, more common in American English where there seems to be a tendency to drop prepositions and even definite and indefinite articles.
For example:-
"Graduate college" instead of "Graduate from college"
"Trump debated Bush" rather than "Trump debated with Bush"
"It happened Monday" rather than "It happened on Monday"

But I may be wrong.

:-))

@jayles - good point. The first page of a site search of The Guardian for "escaped prison" shows mainly the idea of escaping a prison sentence.

"However, they escaped prison after part of the sentence was suspended "
"Anthony Delaney left court yesterday clutching a bag full of belongings. He had escaped prison, but reaped the wrath of the judge at Lewes"

There are a couple with the 'from' meaning, one from North America, and one from a film review.

I agree with others here. If you want to be clear that there was a prison break, say from prison. It brings to the mind of the reader that there was a building or structure involved. Without the preposition "from," it's ambiguous and could mean someone avoided prison.