This is not specifically a Flutter question, more of a general app development question. It's very common to have both local and cloud "storage" but I wouldn't think of it that way. If you're interacting with an API backend I wouldn't consider it as the cloud storage for your app. Instead look at it as a different component within your applications overall architecture. You API/Backend component, this way it's not apart of your app instead it's something your app interacts with.
I assume you know the purpose of your API. Returns your data you want to see, keeps track of user profile information and other sensitive information.
When it comes to local storage I'd say the most common scenarios for local storage is results caching and storing information that the API requires on every session to make the user experience a bit better. See some examples below for both:
- On instagram they store your "Feed watermark" which is a string value that is linked to a specific set of results so that when you open the app and request again they return that set of results, plus anything new - Local storage
- They also "store locally" (better referred to as caching) a small set of your feeds from your posts, a list of user profiles that has stories on them and your DM's for instant and offline access. This way when the app loads up it has something to show while performing the action to get the new information. - Caching
- They also store your login token, that never expires. - Local storage
tl;dr: Yes. If you need data on every session to use your API store that locally in a secure way and use that to interact with your "Cloud storage".