This question was asked in the Formidable forms Slack group earlier today and the answer, although simple, is really useful and versatile.
The code:

<script type="text/javascript">
jQuery(document).ready(function($){ 
$("#field_bttvs").attr("required", false);

$('select[name="item_meta[1601]"]').change(function(){

var isreq;
var val1 = $("select[name='item_meta[1601]']").val();

if (val1 == 'Yes')
    {isreq = true;}
else if (val1 == 'No')
    {isreq = false;}
else if (val1 == '')
    {isreq = false;}

if(isreq){
    $("#field_bttvs").attr("required", true);
}else{
    $("#field_bttvs").attr("required", false);
}});
});
</script>

The snippet above uses a dropdown field and a text field but can be adjusted to use almost any fields.
Replace #field_bttvs with the field key for your text field and 1601 with the field ID of your dropdown field.