The list grows linearly, so I don't think there would be much of a speed issue. You can always set a limit to the total number of calls. For example, if I have 200 friends using your app and you limit the number of calls to 100, only the first 100 friends' friends will be shown. That can be quite an extensive list.
You could also inform your user that the operation he/she is trying to perform might take a while and give them the right to cancel at any time. When they cancel you could display the data you already received.
As a last note instead of using an array to store the friends of friends list, It would be better to use a set because chances are many of those people are already friends with each other. So if "Jake" and "Jen" are friends, they would not appear twice on the list.