How are crisp flavours made?
There is no one answer, as each manufacturer has different processes

Most flavours are simple esters, acids, and salts that mimic the main flavour notes of the food being replicated. Some high quality chips will use actual freeze dried powders made from the actual food

e.g.

Ham powder = the good stuff is freeze dried and then powdered real ham, the other stuff is just fat, smoke, and maybe some chemical esters

Fruit powder = either just the essential chemical ester that denote the fruit, or actual freeze dried fruits. A little freeze dried fruit goes a long way

Cheese powder = spray dried melted cheese, a similar process to how milk powder is made. It's basically cheese with no water

Vinegar powder = acetic acid powder. Vinegar is mostly a ~5% solution of acetic acid, and acetic acid is a common and cheap chemical used in the plastics and glue industries

Chilli or Paprika = capsaicin oil, either naturally extracted, or chemically made, one drop goes a very long way

https://en.wikipedia.org/wiki/Ester

Chip flavours are just "invented" like every thing else. The chips invention is more interesting, see https://en.wikipedia.org/wiki/George_Crum