I’ve seen a few techniques for seeing into the kiln at high temperature. An old friend of mine still prefers blowing into the peephole, unfortunately on more than one occasion it has resulted in the particles resting in the peephole to be blown in as well, settling on the ware. The Jingdezhen firing masters I’ve met just put on an old pair of sunglasses and squint (on the rare occasions they actually need to look at a cone).
I’m currently using #5 welding goggles, the only pair I could find for sale here but they work really well. If you have a choice, go for IR rated lenses which protect from harmful infrared light. Here’s a really good article about eyeware for potters.
Combined with the goggles, a strong flashlight will give you a really good view inside the kiln. This year, my old LED flashlight finally gave out, and at around 400 lumens it was still a little difficult to see in the kiln. The LED flashlight I purchased as a replacement was on sale for about $40USD, a little expensive but to be honest I just wanted to know what 2000 lumens would look like. It’s blinding! But using this flashlight I can see all the way to the back of the kiln even in reduction at 1300° C (my kiln is only 1 meter long). You can even see glazes start to glisten in the light of the flashlight as they begin to melt..
So if you’re getting a new flashlight for the kiln, I think you should go for at least 1000 lumens.