You just love to spread immense misinformation. You should actually educate yourself in this particular matter if you want to write and speak on the slogan. Don’t just blabber your personal opinion, give sources. Your personal opinion doesn’t matter, actual evidence does.
According to Wikipedia article for "From the river to the sea": "Many Palestinian activists have called it "a call for peace and equality" after decades of Israeli military rule over Palestinians while for Jews it is seen as a call for the "destruction" of Israel. Islamist militant faction Hamas used the phrase in its 2017 charter. Usage of the phrase by such Palestinian militant groups has led critics to claim that it advocates for the dismantling of Israel, and the removal or extermination of its Jewish population." So it's not as clear-cut as you suggested. It says some Palestinians define is as a call for peace, but even if it was taken as such in the past, nowadays I have the impression it's mosly used as a defense of the destruction of Isreal. If it was just for the peace of Palestine, they'd use a more specific sentence because the way it's pharsed it includes the Isreal territory in their intentions of "freedom". But they want to be free from what? Free from the Israeli people presence? The article you linked kind of confirm what the Wikipedia article said: each side has an interpretation of what this sentece entails, but I'm more interested in the practical usage of the sentence today, and in my opinion it's mostly anti-Isreal.
Not only that, do you know that Israel has made a slogan exactly like that too. So by your definition; Israel wants to exterminate all Palestinian people (and they’re currently doing so with the genocide).
From the same Wikipedia article: "The Palestinian phrase has also been used by Israeli politicians. The 1977 election manifesto of the right-wing Israeli Likud party said: "Between the sea and the Jordan there will only be Israeli sovereignty."" It seems a variation from "from the river to the sea" was used by a specific Isreali right-wing party in 1977. It was strictly a position of said party in 1977, so we cannot pin it on Isreal of 2024.
Israel flat out said they do NOT want a two state solution.
In the article you linked, this is an opinion of Isreali Prime Minister Benjamin Netanyahu after he got spooked by what occured on October 7th. Who know's what the next Prime Minister will think about it? Israel was explicitly in favor of the Two State Solution in 1937 and 1947, but in both cases the Palestinians refused. Now that missiles are launched from Palestinian territory into Isreal, don't be surprised if Isreal takes a more conservative approach in the name of its national security.
Also explain to us; what is a Hamas flag? I have never heard about it nor seen one. I have only seen the Palestine flag. So tell us, show us and give us actual evidence with reliable sources.