How to stop dealing with flat tires? I have a very nice fixie bike, which I keep suffering from flat tires. I live in Bogota which is a city full of potholes in the road.

I have been examining options to implement in order to have less issues with this flat tires, I got to know this company which is so far the best option I am considering, but it's quite expensive to order a pair of tires just for me, to Bogota.

So I kept checking and I found this videos in youtube 1, 2 and 3 that shows how to do that with a special sealant. Have you tried that in a fixie? Does that work?

EDIT

In more detail:


I suffer a lot of "bite" punctures (so called here) which are two holes in the tube because of a hole or a sidewalk and the rim pressure.
I don't suffer that much of a single hole puncture.
I don't know exactly the amount of pressure, but always that I inflate the tires, are really "tight" you could say.
I ride almost everyday, home-work-home. Each trip around 13km.
I have flat almost once a week. Sometimes once each two weeks.
I inflate the tires at least once a week.
My tires are one year old.
You are correct that the type of puncture you're getting is caused by the rim "pinching" the inner tube. 

The root cause here is one of the following:


pressure too low (most likely) 
You're not avoiding potholes carefully enough
Weight is too high for the tires/terrain.


This has nothing to do with fixies except perhaps that people on fixies tend to awkwardly power through obstacles without unloading enough weight at the right instant in time.

There is junk you can inject into your tubes, but that stuff is terrible and increases rotating weight. You don't need it. Also, this has nothing to do with tire quality. Your rim is pinching the inner tube, not something from the outside the tire.

Suggest you increase pressure on tires and avoid potholes. If that fails to work, try fatter tires. It is OK to go beyond the pressure specified on sidewall.