Possibly, "I do know that" can in fact only be used, when, you are answering the question of whether or not you know the issue at hand (or your knowledge has been called in to question, and you are answering that challenge). Let's say "out of the blue" you wanted to state that "you know that" -- and you wanted an emphatic version.
The string I don't know that is grammatical and common and is used to express doubt. The use of subordinators if or whether after know would suggest a less firm position: he doesn't know or he's not so certain. I don't know that there are bargains yet, but there certainly are opportunities. I don't know that the President has said that he fully supports the conference of the states I don't ...
Examples: I know (about) this difficulty/problem. I know (about) Engineering. In the first sentence, it seems to me that "to know" expresses that the speaker experienced the problem/difficulty before while "to know about" only expresses that the speaker has heard or read about it.
For a non-native speaker like me, I am always wondering how to use you know correctly, as in the following sentence: Alright, well, for example, like on Saturdays, y’know, what I liked to do ...
Cosmopolitan: How to measure your ring size at home: An expert guide
Recently one of my friends told me that there is distinct difference between 'know of something' and 'know about something' expressions. 'know of' is used when you have personal experience with wha...
"Know about" vs. "know of" - English Language & Usage Stack Exchange