At X's expense and of X's timber
Re-read the sentence. The of refers to the gaols, not the prisoner. It means that the jails (gaols) are to be built of the King's timber (wood).
At X's expense and of X's timber
Re-read the sentence. The of refers to the gaols, not the prisoner. It means that the jails (gaols) are to be built of the King's timber (wood).