characters is plural but "their dynamic" is singular so as written it should be "sounds" If it just said "the characters sound interesting" that would be correct
According to The Only Grammar Book You'll Ever Need, if the sentence were: The characters you have described or their dynamic sounds interesting to me. then sounds would be correct because of the or--the subject nearest to the verb determines whether the verb match is singular or plural. If the subject is things joined with and, then the subject is plural.
Yeah, it's a compound subject, and compound subjects are plural. Like, the dog and the cat fight all the time not the dog and the cat fights all the time. Sorry, moose.
Just to let you know, the stumble occurred to me after "dynamic sound" (or "dynamic sounds"). I'm so used to seeing "dynamic" as an adjective rather than as a noun, and "sound" or "sounds" as a noun rather than a verb, that it took a second to recalibrate. So a re-wording might be in order.
I still don't know what the original sample means! It sounds like it means: The characters that you have described sound interesting to me. The dynamic of those characters also sounds interesting to me. But the OP's later remarks suggest that that's absolutely not what it means.
I would say "The characters and their dynamics that you have described sound interesting to me." Or "The dynamics of the characters you have described sound interesting to me."