It depends in large degree upon what you define as the "height" of the Soviet Union. I hate to be so querulous, but the kolkhoz (collective farm) and Sovkhoz (state farm) systems changed to an extraordinary degree between 1940 and 1960. I suspect your answer may be found in Stalinism as a Way of Life: A Narrative in Documents, edited by Siegelbaum and Sokolov. It's a pretty good English translation of 157 documents ─ mostly letters from individual Soviet citizens to authorities ─ that contains some of what you're looking for.

Document 126, for example, is a 1936 document from a dairy herdsman at a collective farm near the Black Sea. Note that the translations in this book take some liberties with English spelling as a way to convey the tone and form in which the letters were written in Russian:

"These are the shortcumings here on the part of the administrashin and the buro for rasing calves: there are no drinking bowls for cows, no towls, no cheescloth. There is no soap during milking [and] no kerosine. The milkmaids dont have overalls either. There never even were any handbasins. There are no troffs for the cows to drink fram at the storehouses. The above mentioned shortcumings may cause losses to our sovkhozes and the whole country too. Maybe I was wrong to write and made mistakes then dont pay attenshin because I cant read or write much."

The sole reference to chickens comes on Page 40, when Sergo Ordzhonikidze reports an incident in the Ukraine in the early years of collectivization:

"The muzhiks were terribly upset when they heard that it looked as though there was a plan to collectivize hens. In one village the muzhiks, finding out about this, slaughtered 125 hens, bought plenty of vodka, and drank while eating the hens: 'Let's gorge ourselves with chicken while we still can.'"

You've asked about animal rights. The conditions described in these two documents date from the 1920s and 1930s, when collectivization was in its infancy, and a particularly brutal program was under way to transform agriculture in the Soviet Union from a private enterprise to a state-controlled (if not always state-owned) one. After Stalin's death, Malenkov and Khrushchev introduced reforms that improved conditions on collective farms. These reforms stagnated somewhat after Khrushchev, and the farms and farming systems in place at the end of the Soviet Union would not have been unfamiliar to a farmer of the Khrushchev era.

If you're asking whether Soviet farms raised chickens in battery cages and close confines, well yes, they did, though not every farm was organized as well as the one in that video from 1974. Soviet farms generally practiced monoculture, with individual farms specializing in dairy production or meat production or egg production.