it's weird that the value is not showing at all as your code snippet should display value. I've created an example below to demonstrate integrating React Context with react-native-navigation but unfortunately as react-native-navigation is not a single root application (each registered screen is a "root") the regular Context pattern would not work as expected.

// CounterContext.js
import React from 'react

const initialCounterState = {
  count: 0
}

const counterContextWrapper = (component) => ({
  ...initialCounterState,
  increment: () => {
    initialCounterState.count += 1
    component.setState({ context: contextWrapper(component) })
  },
  decrement: () => {
    initialCounterState.count -= 1
    component.setState({ context: contextWrapper(component) })
  },
})

export const CounterContext = React.createContext({})

export class CounterContextProvider extends React.Component {
  state = {
    context: counterContextWrapper(this)
  }

  render() {
    return (
      <CounterContext.Provider value={this.state.context}>
        {this.props.children}
      </CounterContext.Provider>
    )
  }
}

// index.js
import { Navigation } from 'react-native-navigation
import { CounterContextProvider } from './CounterContext
import { Main } from './Main

Navigation.registerComponent(
  'Main', 
  () => props => (
    <CounterContextProvider>
      <Main {...props} />
    </CounterContextProvider>
  ),
  () => CounterReactContextScreen
)

// Main.js
import React from 'react'
import { Button, Text, View } from 'react-native'
import { CounterContext } from './CounterContext'

export const Main = () => {
  const { count, increment, decrement } = React.useContext(CounterContext)

  return (
    <View>
      <Text>{`Clicked ${count} times!`}</Text>
      <Button title="Increment" onPress={increment} />
      <Button title="Decrement" onPress={decrement} />
    </View>
  )
}

This should all work, however the caveat is if you register 2 screens with the same Context Provider (for example, Main as your root and Pushed as a screen that gets pushed from Main) if you update the value on Pushed screen, it would not re-render Main screen to show the updated value.

I'd recommend to use MobX if you want Context like API. You could checkout my boilerplate project https://github.com/jinshin1013/rnn-boilerplate.