Flange is an old English Slang term for a ladies vagina. Not commonly used these days, but if you live in the South, you'll mostly have heard it before and have an idea what it means. The male equivalent of this term is Podger.
a 'bit on the side', i.e sex with someone who is not your regular partner. But now taken to mean any female. Because a flange in engineering is a bit on the side of the main thing.