Yes, you can use baby shampoo, but it may not remove the discoloration.
Plain white vinegar is a natural and gentle cleansing, deodorizing and whitening agent. It is also very cheap!
It will leave the feathers very silky and smooth.
When they molt, their feathers will come in beautiful and new.
You can always try a bath with white vinegar and water, but be sure you dry them and keep them warm until they are dry. Apparently lots of people wash their house chickens, and the chickens even enjoy it...and the blow dryer!
ETA...