In some very limited contexts, yes. As the example you linked to ("The one, the only...") demonstrates, the word "only" can be used to mean "best" in a somewhat indirect way by saying that some person, entity, etc. stands alone in their field, implying that they are the first ever to achieve such a high level of expertise or skill, and thus they are, by extension, the best in their field.
However, in the above context (Harry Potter), no. The word "only" means that the folks referred to by "some o' the best" were literally the only ones in their family lines to have magic abilities; no other person before or beside them had such abilities.
This doesn't imply that they were the best magicians. In fact, quite to the contrary, it seems that some other character (the "he" in "what does he know") has implied that Harry's lack of magical heritage is in fact a very bad thing, not a good thing. (If I'm interpreting this correctly; I know little to nothing of the story.)
However, the speaker does state outright that the characters he refers to are "some o' the best [they] ever saw". So while "the only" doesn't mean "the best", "the best" does mean "the best".