Found the answer. Use this code:
$('#useTimeRange').change(function() {
if( this.checked ) { //limit events to timestamp range
//alert("Checked " + startTime + " " + endTime);
var data = {name: 'startTime', value: $("#startTime").val()};
var data2= {name: 'endTime', value:$("#endTime").val()};
$('.flex5').flexOptions({params: [ data, data2 ]}).flexReload();
}
Here's the related UI and firebug: