He is the only one of the persons who is kind.
For most native speakers, using that is also perfectly acceptable. Much to the chagrin of some grammar purists (and no doubt the person who wrote this question), that is routinely used for people and is widely considered acceptable in most situations. (If you need a reference to support that, start with A Concise Grammar of Contemporary English by Randolph Quirk and Sidney Greenbaum.)
The problem with trying to use the plural verb here is that you end up with an incomplete thought. You end up with a subject, but no complement. For example:
He is the only one of the persons who are kind. (?)
All we know is that you have singled out one member of a group of kind people, but we do not know why. To make this a good sentence, you need to add to it what you want to say about that person. You need a complement. For example:
He is the only one of the persons who are kind that drives a Porsche.
Maybe the rest of the individuals in this particular group of kind people all drive Volkswagons.
Also, note that this is an exceedingly clunky sentence that exists only to trick you on some grammar point. It is highly unlikely this would ever be uttered by a native speaker.
Hope this helps.
Student or Learner