I've never seen a glove like this, however.... they still sell chamois in the automotive department (at WalMart and other places). Usually about a 24 inch square for the purpose of drying/polishing your car. Seems like you should be able to fashion a couple gloves or mittens out of that much fabric.
Old-fashioned Hound Glove?
Yes they exist ! I have several, very old now, from the days when I showed but still use them on the boys.
In fact, I turned out my 'dog bag' recently and gave loads of grooming stuff to a young friend. Including another grooming glove - actually a riding glove - the kind with bobbles on the palm. That works very well and then you finish off with the glove you are looking for !
I found mine over the years at trade stands at shows - there always used to be loads of them at Championship Shows in this country but am not sure if they will be permitted in large numbers once showing starts again. There used to be an excellent one you could buy almost anything at - called Petcetera I think. Maybe you can find them on Google.
Hound gloves are essential for grooming Basenjis !
I’ve got one that I had a long time ago when I had a greyhound. One side is a hemp material and the other side is a sisal looking material
I have one that is chamois on one side and cotton corduroy on the other. Can't remember if it came from Petco or a dog show vendor. I've had it for years. Have you tried Etsy?
@zande
Ah, they do exist! I figured that people who show Basenjis would be familiar with this item. Thanks so much for the info - I'll keep searching!
@jengosmonkey
Right, I'd never heard of one either, but it's the recommended grooming tool in a couple of my old Basenji guide books. It's not a brush - looks more like an oven mitt with chamois leather on one side and velvet on the other...
@senjisilly Good idea! I checked. Didn't find a hound glove, but I did find lots of other intriguing dog stuff to spend money on. 
@ann said in Old-fashioned Hound Glove?:
@jengosmonkey
Right, I'd never heard of one either, but it's the recommended grooming tool in a couple of my old Basenji guide books. It's not a brush - looks more like an oven mitt with chamois leather on one side and velvet on the other...
That is exactly what it is, and essential for grooming a Basenji they way they like to be groomed. Especially the old folks. What do you use, @jengosmonkey, to give yours a treat ?
Mine love to sunbathe while they are groomed. You can almost hear them purring -
Seems the modern versions all have a rubber palm with with protruding nibs for removing loose hair, but lack the chamois for polishing. Can't seem to find a Chamois Hound Glove anywhere. After googling them, the search returned returned links to other dog forums that discussed them as well. Like here, people seem to know what they are, but no one knows where to get one. If you have one take care of it. Its seems you are in possession of a unicorn. 