How can I get a high quality profile picture using React Native Facebook SDK GraphRequest?

Try using Graph API field expansion to get the resource:

picture.type(large)

You can also use .height and .width to get an even higher resolution picture or a resolution you need it at:

Example endpoint for 480x{any-width} image: /me?fields=id,name,picture.height(480),[:other_fields]

Example endpoint for {any-height}x480 image: /me?fields=id,name,picture.width(480),[:other_fields]

Example endpoint for maximum resolution image: /me?fields=id,name,picture.height(10000),[:others_fields]

Official documentation is at the /{node-id}/picture page at https://developers.facebook.com/docs/graph-api/reference/user/picture/. And you can try the API out without debugging through the app at: https://developers.facebook.com/tools/explorer/

Here is an example about how we can get a large Facebook user profile's picture on a simple way using the react-native-fbsdk package.

try {
  const currentAccessToken = await AccessToken.getCurrentAccessToken()

  const graphRequest = new GraphRequest('/me', {
    accessToken: currentAccessToken.accessToken,
    parameters: {
      fields: {
        string: 'picture.type(large)',
      },
    },
  }, (error, result) => {
    if (error) {
      console.error(error)
    } else {
      console.log(result.picture.data.url)
    }
  })

  new GraphRequestManager().addRequest(graphRequest).start()
} catch (error) {
  console.error(error)
}