What is the slang word for rich but uneducated people, especially those who live in rural areas and always like to show off?
The more genteel way of describing such people is to employ the French words 'nouveau riche'. At least that is what the educated class in Britain might call them. But if you want a slang term, one might be 'spiv', particularly applied as in 'spiv landlord'. But that has largely gone out of fashion. It is difficult to think of a universal term of any kind which might be used today. To denigrate such people would be seen as politically incorrect, almost tantamount to a form of racism. 'Hillbilly' is rarely used in Britain perhaps because such a social class never really existed. People who have expensive accoutrements, such as cars, but not much substance in education, might be called 'a bit flash'.
A big city person might call them a "Beverly hillbilly". If they aren't really rich but act like they are I hear "hillbilly rich" used - example is a person with a $40K car and $20K home.
Country folk might say they are "too big for their britches" or "high cotton".
The journalist H.L. Mencken coined booboisie (a combination of boob and bourgeoisie) to characterized the uneducated and uncultured people he believed ran the US in the 1920s. While it is not exactly a well-known word today, I believe the word is evocative enough to make its meaning known in context with little help.
Parvenu. It means a person from usually a low social position who has recently or suddenly become wealthy, powerful, or successful but who is not accepted by other wealthy, powerful, and successful people.
Consider Silver-Spoon. From wikipedia (emphasis added):
"The English language expression silver spoon is synonymous with wealth, especially inherited wealth; someone born into a wealthy family is said to have "been born with a silver spoon in his mouth". As an adjective, "silver-spoon" describes someone who has a prosperous background or is of a well-to-do family environment, often with the connotation that the person doesn't appreciate or deserve his or her advantage, it being inherited rather than earned. In Australia the expression "silvertail" is also used, with nearly identical meaning. It has been used in cultural or political situations to describe someone as aristocratic or out of touch with the common people."
While this doesn't necessarily describe the behavior of a show-off, nor imply a lack of education, it can carry that meaning in context. I think the key point here is that it is "inherited rather than earned" -- certainly a condition of an uneducated rich person. And since silver is shiny it can implicate showing-off in the person being described.