Flutter and Dart come with a nice HTTP library out of the box. In my experience, it does everything you'd expect from a networking library. If you're looking for something like Retrofit on Android, there's a package called "jaguar_http" that does the job.
For taking/picking images, you'd use the officially supported "image_picker" plugin. It exposes a nice API based on Dart's Futures and handles Android's onActivityResult dance for you in the background. If you're looking into embedding a camera preview in a Flutter app, there's a package called "camera" for that.
There's generally a plugin that handles the platform stuff you need to do. If not, you can always create one and use Java/Kotlin/Swift/ObjC code to call the native SDK APIs you need yourself. Having published a couple plugins myself, I've found the plugin system to be really nice.