I found this walk in a little book I have in my collection called "Shorter Wild Flower Walks in Dorset" by Peter and Margaret Cramb. At just under three miles it is either a short walk if you are fit or a long walk if you have mobility problems: In general, though, it is easy going with a gentle climb at one point and a couple of styles to cross.
The walk starts from the beach car park (at the end of the road that passes the sub-tropical gardens) and heads east along the South West Coastal Path. The first stretch is along the shingle of Chesil Beach and this is where the most interesting flora is. The shingle is soon left behind as the path turns inland and then skirts the south side of the hill and heads towards the swannery at Abbotsbury.
As you approach the swannery the path turns north, goes through a delightful small woodland, crosses rough pasture, then a stream and leads on to the village of Abbotsbury. From here it is easy walking back along a flower lined lane, retrace your steps along the shingle and return to the car park.
If you want full details of the walk then you will need to buy a copy of the book (if it is still in print?) although you can work it out for yourself with the aid of a good map.