react native how to call multiple functions when onPress is clicked

There are a few ways to achieve this. One option would be to define a function that calls functionOne and functionTwo, and pass that on your onPress handler like so:

functionOne(){
// do something
}

functionTwo(){
// do something
}

functionCombined() {
    this.functionOne();
    this.functionTwo();
}  

<TouchableHighlight onPress={() => this.functionCombined()}/>

Alternatively, and more concisely, you could express functionCombined inline in your JSX like so:

functionOne(){
// do something
}

functionTwo(){
// do someting
}

<TouchableHighlight
 onPress={
  () => { this.functionOne(); this.functionTwo(); }
 }
/>