Defra say you shouldn't feed leftovers/kitchen scraps - following the BSE crisis where infected animals were processed to be feed for cattle, they are keen to prevent diseases crossing between different types of animal.
However, I think most domestic chicken-keepers do as has been done over the centuries: some scraps in the dog bowl, some to the chickens, some in the compost - and minimal amounts in the bin.
I feed my chickens on veg peelings (cooked if potato & sometimes cooked if other things) but rarely plate scraps (dogs), unless it's a bit of tired bread or a bit of rice or pasta - provided it is plain or has a veggie sauce only.
They love the variety and it makes their lives more interesting.
They are all laying daily, but the extras mean they don't get through quite as much pellets. It's my little step towards recycling: we eat the veg, they eat the peel, they turn our reject into yummy eggs.....
So re the aubergine: why not, provided it's not a huge quantity and forms a small treat not a main meal. If they don't like it, they'll certainly leave it.
