Tire removing levers are not needed if you can pull the tire over the rim with your fingers.
The gloves are to keep your hands clean; you'll be grabbing dirty or greasy parts.
You could leave the patch kit at home, and try to repair the flat tube at a convenient time; that tube would become your new spare tube.
In addition to those items, you could carry individually packaged moist towelettes. The gloves normally are enough to keep you clean, but their insides might leave a powder residue on your hands.
Also, if your bike's wheels do not have quick releases, then there are nuts holding the wheels onto the bike. You need to carry a wrench to fit the nuts.
When riding in heavy rain through areas without good shelter, fixing a flat would be unpleasant and could leave unwanted moisture inside the tire. You can find very compact and lightweight emergency shelter tarps at military surplus and sporting goods stores. A tarp would shield you and the wheel as you work.
Notice that these kits often come with more than one patch together on a sheet. It's convenient if, when you first buy the kit, you cut them into individual sections with scissors.
As is often the case, the rubber cement tube shown below had the opening sealed shut with a thin layer of metal. I needed a sharp tool to punch that hole you see in the picture below. If you carry a never-used patch kit when riding, you'd better carry a sharp object also. Otherwise, you'll have no way to get the cement out.
That container is sealed to keep the cement fresh. Don't punch that hole before you need it; the cement inside that tube might be totally dried out by the time you need it.
Periodically verify that your cement still usable. Even a never-opened container of cement could solidify over time, I think.
When your cement is used up or dried, just buy rubber cement at an arts and crafts store.