Can a billionaire buy land in Canada or Greenland and from his own country?
Wha?
Oh, typo. I think the OP means “form.”
No.
I don’t understand what being a billionaire has to do with whether someone can buy land in her/his own country or other countries. Could you perhaps elaborate?
Ah.
No.
No. Land ownership does not convey sovereignty.
Why specify Canada and Greenland?
Why don’t you ask if a billionaire could buy land in the US and establish his own country? 
They’re not real countries, anyway… (BLAME CANADA!)
If said billionaire is capable of defending their claim with force, then sure, they can carve out a bit of Canada (or Greenland or any other state) to form their own country. It probably won’t be recognized by Canada or most other UN member states, and so the best status it can aspire to would probably be comparable to that of other unrecognized (but well-defended and politically functional) countries such as Transnistria, Artsakh, South Ossetia, Abkhazia, and the Turkish Republic of Northern Cyprus. Following these examples, the billionaire’s best bet is to get the backing of a powerful neighbouring country to supply military aid to secure the new country. (Though of course, that’s going to make the country rather beholden to its richer, more powerful neighbour.)
Another option would be to take possession and declare secession of some land so tiny and so remote that Canada simply won’t bother fighting back, except possibly through its own legal system, and only then if the owner uses the land for something flagrantly incompatible with Canadian law. Such a situation would be vaguely similar to the self-proclaimed Principality of Sealand. As with the former option, this isn’t going to result in much, if any, international recognition.
But that “by force” thing is entirely different from the OP, which only talks about the power of the purse as a way to achieve sovereignty.
You can declare your own house a country. The trick is getting some other country to recognize your claim.
The OP is actually pretty vague. They talk about purchase followed by sovereignty, but don’t make any explicit link between the two. What I was trying to convey in my post is that there are some important intermediate steps between the two (namely, an explicit declaration of sovereignty, and enforcing it against the original claimant). Of course, the process of forcibly establishing sovereignty over land need not start with legal purchase; you could just skip straight to the declaration.
You can get a lot further with a large budget and a standing army than you can with a large budget.
I’m going to say no.
Canada and Denmark, eh? I bet one of them will sign an honorary zero-force-of-law “sovereignty” if they come to blows over Hans island and you solve the problem.
His best bet would be to buy Bir Tawil and buy recognition from Egypt and Sudan
What you gonna buy it with if you reject the Government and all their nasty money, surely you can’t use Canadian Dollars or it’s an admission your part of the system.
Maybe find a native who has never dirtied his hand with coin and offer an walrus tusk or something?
Needs answer fast? And s/he’s in Canada or maybe Greenland? 
They’re both countries with incredibly low population densities in the northern remote parts and also unlike other countries that also feature those aspects (like the United States and Russia) wouldn’t really have the military might to do something about it.
Other places you could probably takeover are Svalbard and maybe the middle parts of Australia.
Great and clever idea Asuka.
With little effort hey could buy out an existing failing renegade nation in the Australian outback - the Principality of Hutt River [official website].
Apparently Prince Leonard who abdicated 18 months ago, the late Princess Shirley and Prince Wayne owe the Australian Tax Office some hefty millions. But its not all bad - there’s an established collectable stamp and coin industry and tourist coaches galore and its coming up to its 50th anniversary next year.
After Leonard abdicated, his youngest son Prince Graeme, “Duke of Gilboa, Earl of Canan, GCSOWL., Minister of State & Education, Grand Master of the Order of Wisdom and Learning, Chancellor of the Royal Court, Chancellor of the PHR Royal College of Heraldry & Chancellor of the PHR Royal College of Advanced Research” took over. He announced that financial support for the Illustrious Order of Merit is open and who’d be more meritorious than a billionaire, who could also maybe clear their tax debt?
The PHR office is closed for a couple more days for the Christmas break, so if the billionaire is reading s/he will have some time to sort out their luggage. The weather prediction is for a week of above 30 deg C temperatures, so they wont need to pack the parkas.
Canada has a lot of unused lands. The same for Greenland. I used them as an example, but it could be any nation that has a lot of unused lands, such as Australia.
If a country wanted to take a lot of cash in exchange selling a 40 square mile / 104 square kilometers of land, the government could, in theory, sell it to a private billionaire.
Why his own country? For laws, secrecy, limited taxes, you name it.
Because the USA would never sell any federally owned land and allow it to be formed into another nation.
But with many nations in the world, some of which are struggling, a few billion dollars, and they might be willing to do it.