Yes, it is possible Hermione forgot part of what she read in it.
Hermione remembers a lot of the things she reads, but she doesn’t necessarily, or even likely, remember everything she reads. She didn’t immediately recognize Nicolas Flamel’s name, and helped Harry and Ron unsuccessfully search for him since before Christmas vacation and only figured it out after Christmas vacation was over, although she was apparently familiar with some part of the Philosopher’s Stone since she’s surprised Harry and Ron had never heard of it.
“Nicolas Flamel,’ she whispered dramatically, ‘is the only known maker of the Philosopher’s Stone!’
This didn’t have quite the effect she’d expected.
‘The what?’ said Harry and Ron.
‘Oh, honestly, don’t you two read? Look – read that, there.”
- Harry Potter and the Philosopher's Stone, Chapter 13 (Nicolas Flamel)
In addition, she’d learned about Devil’s Snare from Professor Sprout (presumably in class) but still had trouble remembering how to kill it, she didn’t automatically recall it. That was a more high-pressure situation than finding out who Nicolas Flamel is, but it involved something she would have actually learned in class and still couldn’t remember what she’d learned immediately.
“Stop moving!’ Hermione ordered them. ‘I know what this is – it’s Devil’s Snare!’
‘Oh, I’m so glad we know what it’s called, that’s a great help,’ snarled Ron, leaning back, trying to stop the plant curling around his neck.
‘Shut up, I’m trying to remember how to kill it!’ said Hermione.”
- Harry Potter and the Philosopher's Stone, Chapter 16 (Through the Trapdoor)
Hermione remembered a lot of the things she read, but she also read quite a lot - she didn’t necessarily remember everything she read, but she took in so much knowledge that what she did remember was quite a bit. So, it is possible that she didn’t remember the part about the Chamber of Secrets in Hogwarts: A History. It was a fairly large book, as Hermione describes it as being over a thousand pages long, and there didn’t seem to be any reason she’d specifically remember it over other parts of the book, especially as it seemed to be just a myth and the other parts were facts.
“House-elves!’ said Hermione loudly and proving Harry right. ‘Not once, in over a thousand pages, does Hogwarts: A History mention that we are all colluding in the oppression of a hundred slaves!”
- Harry Potter and the Goblet of Fire, Chapter 15 (Beauxbatons and Durmstrang)
Even if she’d read the whole thing already, she didn’t necessarily memorize its entire contents. They didn’t seem to have studied the Chamber of Secrets in History of Magic, as Professor Binns was reluctant to even talk about it when asked. When the class insisted, he emphasized that it wasn’t true, and that evidence disproved it. It was considered an already disproved myth.
“The whole thing is arrant nonsense, of course,’ he said. ‘Naturally, the school has been searched for evidence of such a chamber, many times, by the most learned witches and wizards. It does not exist. A tale told to frighten the gullible.”
- Harry Potter and the Chamber of Secrets, Chapter 9 (The Writing on the Wall)
Hogwarts: A History wasn’t even a necessary textbook (we saw the booklist and it wasn’t on it), so she was reading it in addition to everything she had to read and absorb for her classes. Reading and memorizing its contents would be lower priority than reading her textbooks and memorizing the information required for her classes, as well as the general information she’d need to remember about the wizarding world still entirely new to her. In addition, the Chamber of Secrets was likely only a small portion of the over a thousand page book, especially as it was considered a legend not thought to be true, as Professor Binns clearly doesn’t think it has any chance of being true. Until it was actually opened, the story of the Chamber would seem fairly low priority to memorize.