First, you need a common borderline. Best focus on cities far from their capital (and ideally close to yours, that increases the probability). Rush cultural city improvements like libraries, cathedrals, everything available. Culture flip probability increases, when there's unrest or a weak (better yet: no) garrison in that city. That's basically it.
The mathematical description for that can be found in the "cultural flip" thread somewhere here. Your overall culture heavily enters, so a huge overall cultural leap (disdainful) is helpful as well.
Culture flipping still remains a strange subject. I had a looong common borderline with the zulu (me playing the scientific persians) and we were constantly disdainful of their so-called achievements. Not a single flip for more than 3000 years until I lost patience and whiped them out in two consecutive crusade. Strange enough, after the first crusade (took bout half of their cities), one of the invaded cities flipped back to them, despite my huge lead and constant rushing of improvements. Any explanations?
From looking at the formula, there are only two things that can cause a city to flip. The first cause of flipping is having another civ's cultural borders within the city's radius (the "fat X" of tiles that the city can work). If your cultural borders don't reach into the other city's radius, it will never flip. The number of squares of overlap affects the likelihood of it flipping. I think this is the only way in which building cultural improvements in nearby cities helps in flipping or preventing flips.
A city can also flip if it contains citizens from another civ. So any captured city can flip back to its previous owner even if it is far from unfreindly cultural borders. The number of foreign citizens affects the likelyhood of of the city flipping, with resisting citizens counting double. And cities in disorder are more likely to flip. So when you take a city, it may be best to turn everyone to an entertainer to starve the foreign population and reduce the chance of fipping.
Your total culture and the city's proximity to your capitol and your opponents's capitol also strongly affect the chnace of flipping, but do not actually cause a city to filp. Stationing units in a city can prevent it from flipping, but it takes a lot of units, 10 may not be enough even for a medium-sized city.
At least, that's how I understand it. The formula is more specific, so check that out if you want to know exactly how it works.
I've never seen it mentioned anywhere but I always build my forbidden palace in a border city and flips seem to follow. Whether this is the FP causing the flip or if it is just the result of the lower corruption allowing me to build my improvements faster I just don't know.
Good wee tip for flipping (works well against zulus and english (expansionists don't build many improvements but seem to secure a lot of luxuries)) Is to cut any roads in no man's land that connect their border cities to the rest of their empire. Suddenly they slip into disorder and flip. Nice one.
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