I managed to overcome this by doing the following.
Pick the font size you like for the current view you have (Make sure it looks good for the current device you are using in the simulator).
import { Dimensions } from 'react-native'
and define the width
outside of the component like so: let width = Dimensions.get('window').width;
Now console.log(width) and write it down. If your good looking font size is 15 and your width is 360 for example, then take 360 and divide by 15 ( = 24). This is going to be the important value that is going to adjust to different sizes.
Use this number in your styles object like so: textFontSize: { fontSize = width / 24 },...
Now you have a responsive fontSize.