There's no such thing as a burn in time, in the sense that an electronic circuit behaves differently after say 100 hours of use.
There can be a temperature effect though. An amplifier (and also other equipment) warms up when switched on. All components slowly reach their stable temperature and the electronic operating point that belongs to that temperature. Depending on the circuit there may or may not be subtle audible differences between cold and warm operating state. Some prefer to keep their gear switched on 24/7.