The conflict in the short story Condensed milk is survival in a Gulag, hunger, and desperation.
Explanation:
The story follows Shestakov, a camp geologist who asks a miner to help him escape the Gulag. The miner knows the task is impossible but because he is hungry he agrees to do it in exchange for 2 cans of condensed milk.
Many prisoners attempt to escape with Shestakov but are captured and some of them are killed.
In this story, the miner walks into sure death just to have condensed milk once. The desperation and perennial hunger of the gulags pushed him to trade his life for some food that is usually a staple in normal people's lives.
This hunger and desperation is the main conflict of the story.