Been a while since I was up that way but you should be able to get to Platypus Flat from Timmsvale via Ulong & Cascade. Take the Eastern Dorrigo Way west out of Ulong. Turn onto Lower Bobo Rd, then onto Morora Rd after crossing Bobo River. Near Cascade turn north onto Moses Rock Rd. Turn west onto Cedar Rd & follow that to Platypus Flat Rd. Should be around 30 km from Ulong to Platypus Flat.
Don`t think there are any short cuts from Platypus Flat to Billys or Cloud Creek. Only road I know of comes out at the Tyringham- Dorrigo Rd.
Are you aware that you need to book a campsite at Platypus Flat? - http://www.nationalparks.nsw.gov.au/...lat-campground
PM your email address if you want & I can send you some Google Earth track files.