Hi Michael:
This whole scenario sounds a little odd to me. The reason is that I don't think I would work to de-sensitive Babylon in the manner you describe because my presence is usually "desensitizing" enough. Basically, she allows me to handle her, pick her up, etc. because she has such a strong trust in me. In other words, if she is frightened or spooked her immediate reflex is to get as close to me as possible. She also tends to be even more compliant than normal. She rarely flies away from me and if she is in a "stressful" situation, she is extremely unlikely to fly away from me. In other words, she anchors herself to my presence and she uses me - my nonverbal and verbal communication - as an aide to understand the risk she would associate in new locations. I never chase her. I don't chase any of my birds.
In a new environment, Babylon has taken off for what looks to me to be a "mapping" flight. She doesn't land on any object. She just flies big circles around the area, and then she finds me and she flies back to me. I think she feels secure in the air but I also think she feels insecure if I am out of sight....so, she's pretty quick to turn back around and land on me. You can see her doing this sort of thing on my youtube videos:
If Babylon flies away from me, it is seldom because she is insecure but instead, it is when she is extremely comfortable in the environment. She anchors to me and when she feels safe, then she goes off and explores the environment. Both of my hens watch me very carefully for any "cues" from me that something is not "safe" and they fly back to me immediately. You can actually see them approach a new object, look to the side and look at me, approach the object a little closer, look at me....and if I say "ah....ah..." they will fly away from the object and fly to me. I really think this is what you want to train for.
In terms of "spooking"...I want my birds to spook if something frightens them. I want the birds to understand risk or danger and fly away from it. If we are in an unfamiliar situation, the trick is to train the bird to fly BACK to you immediately. I never want the bird to associate my person with "risk". Babylon has always offered boomerang flights but I had to train Phinney (TAG). I felt that this was the most important thing I could train Phinney for her safety because I do take her to unfamiliar locations and if a dog or cat approaches, I want her to know that she can fly away from that animal but she should also center on me, look for me and fly back to me. This is a very healthy response.
I am curious about Kili's flight response. When she startles, does she fly away from you? If so, I think this is where you should be focusing your training. You should be focusing on having her return to you when she startles. This part is about more than operant conditioning. It is really about the "setting conditions" for the training. It is making sure that the bird has established absolute trust in you and in your training. I do think that the best thing for the bird is for the bird to understand that they have some autonomy and that they can act for their own safety.
Just my two cents on this.....I think it's good to have a parrot that flies away when they are nervous. That's what they evolved to do. Our challenge is two-fold: First, make sure that they are less nervous in unfamiliar environments because they have established trust in us to watch for them and to protect them and Two, to work hard to make sure that once they do fly, that they come back to us.
Thanks