I use a Polar H10 as well but use it with my Coros Watch. I have a Coros and TP app on my phone. After the workout, the workout gets uploaded from my watch to the Coros app and then to the TP app.
Apple Health App vs. Polar Flow – I haven’t used them so can’t comment on which is better. You will have to figure out a way to sync your workout with TP. Installing TP app on iPhone and then syncing it with Apple Health or Polar Flow might be the easiest option.