Disable caching for custom entity
The flag you are looking for is persistent_cache, field_cache is no longer used, that documentation is a bit out of date. You're welcome to update it :)

See the API documentation of the EntityType class for a up to date list, maybe that documentation page should just link to that instead of trying to maintain a duplicate list.

That said, unless you have almost as many or more writes/changes to your entity type as loads, I'd considering changing your architecture and either update the entity type through the API or invalidate the changed entities. But there can be cases where that doesn't make sense, e.g. because of mass updates and if those entities aren't very frequently. But for example displaying them in views can be quite slow if they need to be loaded all the time.

Also, speaking of views, while render_cache disables the caching of viewing an entity, I don't think it disables views row-level caching. Maybe it should, you should consider opening a core issue for that if you need that, otherwise your rows will still return cached output even if the entity is changed.