tl;dr: Dissolution of Parliament in the UK happens either at the end of a five year term, or when the Prime Minister initiates it. In the latter case, the PM "requests" that the Monarch authorizes a proclamation to dissolve Parliament.
What a garbage, click-baity headline. The article lists only like 5 of these supposed 23 tweets, doesn't provide links to go see them yourself, and none of them mention King Charles, or overthrowing the government. From what I read in text that IS there, "overthrowing the government" is entirely not what he's calling for, he's basically saying they should hold an election to oust the current parliament leadership.
This has to be one of the most jounalistically-bankrupt articles I've read in years.