Hi Andrew, Itchy skin eh? Well it could be your basenji's diet causing a food allergy, could be the soap you bath him in if you have bathed him, or could be something in your house.
The easiest and cheapest thing to do is to change the environment one thing at a time and see if there is improvement.
Try switching the bedding to a towel.
Try bathing him with a non soap shampoo.
Feed him boiled chicken to test if it is his food.
These are just a few suggestions.
Caesar and Beta both had very scaley skin one year and it was probably the Eukanuba I was feeding them. The vet gave me oil supplements to add to their diet which fixed the problem. Later on I found out that there are better foods out there than you can find in Petsmart.
The best thing to do is be very observant and rule things out so that when you talk to your vet, you have better information.