Thought I would share my solution using a function component... 'this' not needed!
React 16.12.0 and React Native 0.61.5
Here is an example of my component:
import React, { useRef } from 'react'
...
const MyFormComponent = () => {
const ref_input2 = useRef();
const ref_input3 = useRef();
return (
<>
<TextInput
placeholder="Input1"
autoFocus={true}
returnKeyType="next"
onSubmitEditing={() => ref_input2.current.focus()}
/>
<TextInput
placeholder="Input2"
returnKeyType="next"
onSubmitEditing={() => ref_input3.current.focus()}
ref={ref_input2}
/>
<TextInput
placeholder="Input3"
ref={ref_input3}
/>
</>
)
}