I think you will find your answer on this post here:
http://www.flextutor.org/flex-tips-suggestions/custom-tickinterval-and-snapinterval-in-a-flex-slider/

This seems a bit weird, but I think it does what you’re looking for:

<?xml version="1.0" encoding="utf-8"?>
<mx:Application xmlns:mx="http://www.adobe.com/2006/mxml"
        layout="vertical"
        verticalAlign="middle"
        backgroundColor="white">

    <mx:Script>
        <![CDATA[
            import mx.events.SliderEvent;

            private function slider_change(evt:SliderEvent):void {
                if (evt.value > 0) {
                    slider.minimum = 0;
                    slider.value = evt.value - 1;
                } else {
                    slider.minimum = 1;
                    slider.value = 1;
                }
            }
        ]]>
    </mx:Script>

    <mx:HSlider id="slider"
            minimum="1"
            maximum="100"
            value="1"
            snapInterval="5"
            labels="[1,25,50,75,100]"
            liveDragging="true"
            dataTipPrecision="0"
            change="slider_change(event);" />

</mx:Application>

Peter