The Invisible Man
If Kemp is the hero of this book, then we are in serious trouble. Sure, there are some things that are heroic about him. For example, he's smart and quick to action. After Griffin escapes from Kemp's trap, Kemp quickly explains to Adye how they can capture him: dogs, locked houses, and powdered glass on the roads.
Let's be serious, though. In almost every way, Kemp makes a pretty lousy hero. First, he makes a lot of bad decisions. We especially like when he sends out a note to the police, without thinking that the Invisible Man might intercept it (27.5). That doesn't end well. It's also not like he's a very brave fighter. When the police fight the Invisible Man, Kemp runs away (27.88). On top of all that, Kemp is well-off financially (he has servants and doesn't need to practice medicine to make a living [18.19]), so he can't even play the underdog card.
So What is He Doing Here?
Though Kemp is hardly heroic, he is the major opponent to Griffin. Without Kemp's help to the police, Griffin would probably have been more successful in his Reign of Terror. Because Griffin tells Kemp his whole story, Kemp knows his weaknesses (and he doesn't hesitate to exploit them).
So Kemp is almost a plot-mover of sorts: he gives Griffin a reason to tell his back story (which helps us, since we don't know anything about him up to that point), and he's prevents the IM's takeover in the last third of the book.
What Does it Say on his Business Card?
Dr. Kemp is a scientist and speculative philosopher. Okay, let's break that down a bit.
First, scientist: Kemp may be Griffin's opponent, but they are both scientists. When we first meet Kemp, he's surrounded by scientific publications (15.1). What's even more striking is that he wants to be part of the Royal Society (15.1), the famous scientific organization. In that way, he's even more like Griffin, since they both want recognition for their scientific achievements.
Second, speculative philosopher: Kemp's science doesn't use as many bottles as Griffin's. (Although he does have a microscope and slides [15.1].) Instead, Kemp spends more of his time, well, speculating. For instance, the night that Griffin comes to his house, Kemp is working on "a remote speculation of social conditions of the future" (17.4). (That's not the kind of thing you can run an experiment about.) If Kemp's interest in science makes him seem close to Griffin, then his speculations about the future make him seem close to Wells. After all, Wells wrote several essays and The Time Machine about "social conditions of the future."
So who is Kemp, really? A hero? Another version of Griffin? Or a stand-in for Wells?