Cloudinary is the easiest and most flexible way to do this. It’s not super fast, though.
If you wanted to use an API to store them on your own server then you’d need to provide the endpoint documentation for that and someone here could help you. But I’m not aware of an API that generically stores images wherever you want.
Is there a reason you’re not wanting to use Cloudinary?
I don’t wish to use a paid service. I can host all media on my server. If and when this App grows to be a Paid Membership type, then I will consider using a third party premium service.
I can create a Rest API script on my side but don’t know how to POST from Thunkable. If use POST for Login etc etc but not to upload a binary file.
This will read an image file and {{upload}} it to the app but you can save it anywhere you decide to. Use it from a mobile device and click Choose File to select the file.