The meaning of "Not but what it might have been for something else; but it warn't."?

Solution 1:

Not but what is another way of saying Nevertheless.

Nevertheless

in spite of what has just been said

(MWD)

So, instead, the sentence could read:

"I had come out of Kingston Jail last on a vagrancy committal. Nevertheless it might have been for something else; but it warn't."

Which means that, despite what was just said, the speaker could've been in jail for something else, but wasn't.