How to transfer cloud data to new phone from old phone that won't turn on

If the data is on the phone itself, and it is the phone that doesn't work, then you can't get any data off of it.

Now if you had, previously saved or synced the data to the online/cloud account before the phone went bad, then you could download it from that account by just logging into it from the new phone. Without that, there is no access to it.