I've been having the same issues with an arch-derived distro and it also gets stuck, leading me to believe that the issue's on flatpack's distribution end.

(I use shelly for my updating, and it works fine for pacman and AURs, but at least for the past day it's hung up on flatpacks. I also tried running "flatpack update" in bash with no results.)

Because of that I don't think there's any solution other than manual installation until Flatpack solves the distribution issue.