Does this sentence use correct grammar You should of known better.?

No, the sentence "You should of known better" is grammatically incorrect.

The correct sentence is: "You should have known better."

Here's why:

* "Of" is incorrect: "Of" is a preposition and should not be used in this context.

* "Have" is the correct auxiliary verb: The phrase "should have" is used to express regret or reproach about a past action.