He's 35 and he's been doing this since he left school? So 17 years or so?
"My BiL has two problems, his wife thinks they should continue to support their son even to the extent of using their savings. They adopted him when he was a baby and when BiL has tried to reason with him in the past he has flown into a rage and pulled the "you're not my real parents so can't understand" argument."
So really, there's two people that need talking to here - your BIL's wife, and their son.
BILs wife obviously wants to support her son, so must be made to see that by just continuing to give handouts, she is doing exactly the opposite. She is infantalizing him, keeping him dependant on her - she needs to see that cutting the apron strings is the best thing she can do FOR HIM as well as for her husband and herself. Ask how she sees the future panning out - will her son marry and have children? Does she want grandchildren? How will keeping her son on handouts achieve his long-term happiness? I'd even be brutal enough to ask how he will manage when they are both dead. Because barring her son having a fatal accident, that is inevitable, isn't it? How will he live then, since they will have chewed through all their savings trying to support him? He'll be flung onto his own resources with no experience of making his own way. Surely it is better to wean him off handouts now, while they are still their to give practical and emotional (as opposed to financial) assistance? Why would she want to leave him helpless? Yes, this is laying it on with a trowel and guilt-tripping her; but if she can't see it for herself then that's how to get it through to her.
And the son? I wonder if it would be worth turning his own words back on him. He throws "you're not my real parents so can't understand" at them; BIL responds along the lines of 'if you don't feel I'm your father, maybe that's why you don't care that my health means I can't work any more. Is that how you feel about us? That you don't care about us, we're only good for money? That hurts, son.' Again, brutal and trowel-ly, but possibly necessary. I do wonder if your BILs wife already feels at the back of her mind that her son doesn't love her.