While the actual Twitch vod may be gone forever (I honestly haven't looked too hard to see if it was clipped anywhere because this comes up rather infrequently now), @The Mass Shooter Ron Soye was kind enough to provide a written transcript of the pertinent parts the night of the stream (January 18th, 2020). You can peruse that
here.
Of particular note:
"These fucking harlots," in this context, meaning Jamie and Monica. See earlier in the above linked transcript.
So yes, he
absolutely tried to get Vic to come on his show for the expressed purposes of shitting on the KV defendants, and was pissed when Vic said no.
I am of the opinion (and I don't think I'm alone here) that that was a stupid fucking move on Nick's part, and Vic was correct to demur. Had Vic done what Nick wanted, he would have only gotten even more heat, and suffered more reputational damage, while still ultimately still losing in court thanks to Ty's incompetence.
Nick wanted a fiery Vic appearance, because he is a selfish fuck and knew it would draw a paying crowd. Nick uses people for his own ends with little regard to any deleterious effects it may have on the person he is using. Like @AnOminous said, that cringe Twitch rant was an example of an early mask slip. He has only gotten way worse, and infinitely more obvious, since then.
EDIT: Cleanup and clarification.