The answer is... you don't.
I searched for a simple way to delete FamilyEcho history but found there's no direct option. Creating a new tree seems like the easiest workaround. Hope FamilyEcho adds this feature soon.
Hi nmichalo, if you mean the history or family tree you’ve created, you can usually manage or delete it from your Family Echo account settings. I’d recommend checking the FAQ or account options first for the exact steps. OK