I think my children are privileged - but I am not sure how one defines it. In our case, we are not rich compared to many but we have more than we need IYSWIM. We own a mortgaged 4 bed house (not SE), we have a cleaner, 2 cars, holiday abroad every other year etc. But we are not higher rate tax payers, kids are in state education and so on. They have loving and interested parents, access to extra curricular etc - all of which in consider to be privileged compared to so many.
It is monetary though , or is it greater than that? Like a pp poster said, my childhood was more affluent than my children’s , but not a happy one. My partner’s childhood was much more modest but she did not consider they lived in poverty - council house, caravan holidays etc. More stable and loving than mine.
And where does innate privilege come into play? We are both women - but we are also both white.
However, my childhood was very ‘middle upper class’ I suppose , so I ended up with the private school confidence, queens English etc. OTOH, my partner grew up in an area where women were expected to work in a shop or factory until they married - or if they were attractive and clever, become a secretary. And therefore educated accordingly. Plus a strong regional access that people judge. She is more intelligent than I am, but many people still assume the opposite, based on judging educational achievement, confidence and being articulate. My children have a combination of this - although they will have the opportunities that my wife did not.
On balance, I think my children probably have more privilege than either of us did.