I'm far from an expert on budgies, but I think that flying away is a natural thing for them to do. Keep up your attempts at bonding and I'm sure they'll stop flying away from you and eventually start wanting to fly to you! If you're following Roland's SEAT method (I am, on day three and getting great results!) it's recommended that your bird be able to fly away from you. A this point it's probably not quite sure if you're a predator or not, but over time it will come to think of you as a beloved flock member!
As your bird gets more confident and feels secure with you (bonding) they will be more likely to stay on your finger. In saying that, if you want your bird to stay in one place then it needs to be interested for them. This is the general basis behind Roland's method. If you are wanting your bird to stay on its cage, have you set up a play gym on it?
If you spend a lot of time with him at first in a small space where there is no place to fly to, he will gt used to you and start to enjoy hanging out with you. I have made a video all about it here https://www.youtube.com/watch?v=y_Js...e_gdata_player its a long video but I explain everything and show what to do. I got. Tent so I don't have to use the closet. Now that same budge will sleep on my finger because he is comfortable with me.
The next step is to hold him in a biger room, like your bedroom. They will fly around and won't know whre to go. Johnny here flew into the tv several times, so I picked him up and touched the tv with the finger he was standing on (same if its a window) and tapped it wih my other hand to show it is solid. Then I walk around the room with him in a circle to show a pattern he can fly in. Now Johnny will fly around the room in a circle and return to my hand/shoulder every time. It is cool to teach flight triciks because they can get energy out and be calmer when they come back to sit on you. Johnny will be chilling with me and then let out a little "reeht reeht reeht!" noise before he takes off and circles the room. If you play it cool, they will come right back to you and be more relaxed. It only works if they are really bonded to you first like I show in the video. I have another video on that channel called "how to handle a tame parakeet" and that shows how to handle them when they are mostly tamed. That bird is clipped so I couldn't teach it fight tricks. But I show how to keep them off your head ad tuff like that.
This is a great question. There are different ways people address it, I am just showing what I do. This has been great for my birds because if they accidentally get outside, it is easy for me to catch them. I just stand there and they fly back to me since its part of a drill they know. That is not something I would practice with a bird (going outside) until I have been bonding for 6 months to a year. It is still risky for beginners. But in an emergency, it can save your budgie in case they go outside by total accident.
I watched the video and found it very helpful, and inspirational!
After I saw it, I got my budgies out of their cage with nutriberries in my palm. I took them into another room and they sat on my shoulder and crawled all around my shirt. After about fifteen minutes, I came back in the livingroom and sat next to where their cage is. They stayed on me for another ten minutes or so. They were really relaxed. It was So Amazing! Thank you for your video.