I personally feel that it is a mis-attribution and will be unfortunately carried on to future generations of the new owner's family. The set of 3 appear to have been produced in a later era (20th century) than either of those makers were active. I'd love to get a chance to look at the hardware and nails/screws which would help date it more accurately.
I think you may have been reminded of the Bembe & Kimbel chairs due to the Guilloche pattern on both. If you sniff around you'll see many examples that are similar throughout history
, so isn't an identifying feature to attribute solely to B&K.