What the Flanaess does have a lot of material on is heraldry and of course knighthoods and titles. The bulk of it is listed in the last couple pages of the boxed set guide with enough details to provide a framework for a cross-nation system of jousting tournaments:
The Knight Protectors of the Great Kingdom are called exceedingly formidable but those in Medegia are looked on with contempt because the title is for sale. Given the size and history of the Great Kingdom of Aerdy I can see their tourneys being tied down to their own provinces and cities, with all the bluster and intrigue you'd expect from an evil realm. The Great Kingdom has numerous noble houses to start with in forming tourneys, one only needs to get a download of Ivid the Undying to get a wealth of info. The religion of Hextor would also factor heavily into these competitions since the simulation of combat is what keeps the knights busy when the Greyhawk Wars aren't raging.
Someone wanting to run a campaign centered on jousts in the (pre-wars) Great Kingdom could follow a circuit like this for example: Start in Eastfair in the North Province then southward to Delaric, Jalpa, Rel Deven, Kalstrand in the South Province and back east to Nulbish, Torrich, Mentery (those despicable Medegian knights), and back up the coast to Rel Astra and perhaps Roland then ending in the capital of Rauxes.
Now for the "true knighthoods" according to the Greyhawk Guide, there is the Knights of the Watch in the Kingdom of Keoland area, the Knights of the Shield in the Shield Lands and the Knights of the Hart in Furyondy, Veluna and Highfolk. How these orders get along is mentioned in the last paragraph of the book.
"Knight of the Hart are hated and despised by Iuz, the Horned Society, and even by the folk of Dyvers, it is said. There is no love lost between them and the Watchers, the rulers of Perrenland, and certain of the Nyrondel noblesse. Considerable rivalry exists between the orders of Hart and the Shield."
So the three branches of Hart and the Holy Shield knights, in their downtime from fighting the evil of Iuz could easily tour the good lands of the north, possibly including the Kingdom of Nyrond (whose cavalry is legendary for defeating the Aerdy at the Battle of a Fortnight's Length) and Perrenland (who seem rather upset at the knights for having more prowess at arms than them?). The knights of the Shield and Hart probably butt heads a lot during war, but during the tourneys their rivalry is friendly and honorable. I'd also say the two orders would be equal in skill if not size. I've personally ran a tournament campaign in this region before and it worked out incredibly well.
Lastly, to the south you have the Knights of the Watch who have a bad history with the Ferrond-Veluna nobles and knighthoods so they'd be rather reluctant to take part in cross-nation tourneys (though I could see demi-human realms like Highfolk and the Uleks as being moderators between human orders). These Watchers are much more numerous (ten times roughly) so it would follow that their jousting skills wouldn't be as good as the elite teams of Hart and Shield knights. Then again, with a larger population of fighters to draw from perhaps the Lion Throne would dominate a tourney circuit or host theirs own entirely like the Great Kingdom. Such a circuit could cover several states in a year going from Yeomanry, Sterich, Geoff, Keoland, to the three Uleks and Gran March.
A grand jousting campaign would combine all the major kingdoms into one long circuit where you could start in the west with Niole Dra and arc your way across the Flanaess hitting all the capitals like Mitrik, Chendl, Amundfort, Rel Mord, and finally Rauxes (where a war then erupts when the Aerdy loses). This area encompasses a breadth of almost 2000 miles east-west unfortunately, so it doesn't seem probable that knights would tour that far from home unless they are individually questing knights or paladins.
One more tidbit, I like this Tournament Ranking chart from the Companion Rules; make use of it to entice your players into trying out jousting:
Tournaments Won Title
15 Silver Champion
20 Premier Chevalier
25 Grand Champion