Just going to have a stroll along the coast from RHB to Whitby tomorrow. Not familiar with the cinder track but sounds good to make it a circular walk. Presume it is the old railway line. Where do you pick it up in Whitby having dropped down from the Abbey?
When you drop down from the Abbey, go through the town and over the bridge where the harbour is and turn left, towards the station. At the station roundabout go straight on, the station should be on your left. This road climbs up for a bit until it reaches a small roundabout. You want to walk slightly to the right and then cross over into a road called Southend Gardens and walk 100 yards or so up this hill and you'll then see a tunnel ahead of you (old railway bridge) and steps to the left of it, climb these and you're at the start of the Cinder track, hope that helps. Here's a screen shot of the route.