Which detail from the passage supports the claim that this is an allegory for the great purge ?

I think it is the third one. But investigate yourself before taking my word for it because I am not completely positive :)
Answer:
The protesting hens being intentionally starved.
Explanation:
The Great Purge was a period of political repression in the Soviet Union, from 1936 to 1938. During these years, police surveillance, imprisonment and executions were common. The purge was designed to eliminate all opposition to the Party and the party's objectives. In this excerpt, the fact that the hens want to rebel, and that they are intentionally starved, resembles the Great Purge, and the extreme methods that were used in order to eliminate opposition to the Communist Party.