Retro chic is a style that draws on influences of a by-gone era. You need to find quality vintage items with bright patterns - red with white spots, or big, red polka dots, for example. Materials are important to, retro chic items will be made of cotton and natural linen, rather than using man made fabrics Plastic is not acceptable, but melamine and bakerlite are.
To become 'Retro Chic' you need to build an eclectic collection of items - look in flea markets, charity shops and second hand stalls. Think of the 1950s in particular, but also the 60s & 70s, but any styles post 1979 would not really be retro chic.