Both the birds and the environment need treating, as they live on the bird, and eggs and larvae can also be on the ground. They are a serious nuisance to the birds and quite difficult to get rid of. There are a lot of different products that can be used to treat the bird. Some people suffocate the fleas with olive oil or baby oil, but most find it easier to use moxidectin or ivermectin. The coop and floors need spraying, especially if you have dirt floors as the larvae live on it. The cages, pens, perches and surrounds should also be treated by spraying with a solution of Malawash (Maldison), or Pyrethrum, or Permethrin, or CoopX etc. Some people prefer not to use the Malawash and choose one of the others as it is quite a toxic chemical. The Permethrin or the Pyrethrum are good choices. There are plenty to choose from, and I'm sure you're local produce store will carry something that is suitable. All the litter needs replacing after you spray.
There's a lot of information about stickfast fleas in this thread. Have a read through.viewtopic.php?f=5&t=8196&hilit=stick+fast
The witholding period for eggs depends on which product you use. Read the manufacturer's instructions.