Hello!
The original form of "богатенькие" is "богатые" - rich people, who have much money and can afford themselves whatever they want. We use the suffix "еньк" in order to get a diminutive form, or to show some kind of irony.
For example, there is a russian idiom "богатенький Буратино", which describes a man, who has gotten his wealth by chance and spend money unreasonable.