A look at the KC website will show you a myriad of screening schemes for many breeds. Currently the whippet is not a part of their screening programme.
As you are aware, some breeds of dog (and crossbreeds too) can be susceptible to inherited disease. DNA tests for diseases in purebred dogs are available for some conditions in some breeds.
Whilst there are not a large number of such tests as yet, more are being developed on an increasingly regular basis as scientists gain a fuller understanding of canine genomics. There are also a number of other clinical veterinary screening schemes that dog breeders can use to increase the probability of producing healthy puppies