Common styles in React-Native
While sharing styles is possible, I find it a little cumbersome and personally, I would not do it. Instead, I'd recommend going one level higher: do not share styles, share components.

That's what React is about - sharing components. In React Native, you won't have to import a component and styles (and pass the styles to the component), you'll just have to import the component. There will be less duplication.

I'd recommend you take a look at styled-components or glamorous-native, and see their utilities for defining styles, extending them and other utilities. They will make working with styles and components easier.