How can I change the list position of people in Find My app list on iPhone

As far as I know, there is no set order for how the list of people show up in the Find My app. It is entirely random. What you can do is star certain people and they will appear at the top of your list. Swipe left on a contact to do so.

You are also welcome to provide Apple with your feedback regarding this, so they know what you and others want and may possible add it in a future update. Feedback - iPhone - Apple