Possible meanings are 1) "Know this" is a command to pay attention to what I am about to write or 2) "You know this" is a statement saying that I am about to remind you of something that you already know.
These sayings are idioms that mean people should first listen intently, and then consider carefully what they say. Here "slow to speak" does not mean speaking slowly. (See: [[rc://en/ta/man/jit/figs-idiom]])