I'm not really sure of the syntax {el => this.inputEntry = el}, but when clearing an input field you assign a ref like you mentioned.
<input type="text" ref="someName" />
Then in the onClick function after you've finished using the input value, just use...
this.refs.someName.value = '';
Edit
Actually the {el => this.inputEntry = el} is the same as this I believe. Maybe someone can correct me. The value for el must be getting passed in from somewhere, to act as the reference.
function (el) {
this.inputEntry = el;
}