In the series The Dark Crystal: Age of Resistance, each of the Skeksis have different sounds in their speech, such as a slight British accent, although most seem to have American accents, except Chamberlain. He speaks with broken English grammar. Why? They've been on Thra for a thousand trine, and none of the Gelflings or Skeksis have any accent or speak any other dialect. And the Skeksis tend to speak mostly within their own kind. Why, then, the accent?
I assume you've watched the movie...
If you haven't this will be a spoiler..but the movie came out 30 years ago.
Anyways....The Skeksis and the urRu are actually split creatures from an immortal race of aliens called urSkeks. Weird things that we only ever see a couple of at end of the movie. When attempting to use the Crystal they ended up splitting themselves into each respective creature. Meaning the personality and existence of each is a combination or split of the original urSkek. This is the only in universe explanation of why each character is who, or rather why they are. The Chamberlain's counter part urRu likely got the better vocal chords in the deal.