How do I clean a cheap blow torch?
I have doubt it's even the tip clogging - could be a valve failure and have the described symptoms. I have never needed to clean the orifices on a propane torch, and I've been using them (the same ones, for the most part, other than having them walk off sometimes) for decades. Oxy-acetylene, yes - those can and do get sooted up. Propane/propylene-air - never.

Sometimes "cheap" is expensive, and "costly" is inexpensive.