Full code after the jump.

View MXML

<?xml version="1.0" encoding="utf-8"?>
<!-- http://blog.flexexamples.com/2007/12/16/changing-the-next-and-previous-month-navigation-icons-on-a-datefield-control-in-flex/ -->
<mx:Application xmlns:mx="http://www.adobe.com/2006/mxml"
        layout="vertical"
        verticalAlign="top"
        backgroundColor="white">

    <mx:Style>
        .myDateChooserStyles {
            /* Previous Month */
            prevMonthUpSkin: Embed("assets/bullet_delete.png");
            prevMonthOverSkin: Embed("assets/bullet_delete.png");
            prevMonthDownSkin: Embed("assets/bullet_delete.png");
            prevMonthDisabledSkin: Embed("assets/bullet_delete.png");

            /* Next Month */
            nextMonthUpSkin: Embed("assets/bullet_add.png");
            nextMonthOverSkin: Embed("assets/bullet_add.png");
            nextMonthDownSkin: Embed("assets/bullet_add.png");
            nextMonthDisabledSkin: Embed("assets/bullet_add.png");
        }
    </mx:Style>

    <mx:DateField id="dateField"
            dateChooserStyleName="myDateChooserStyles" />

</mx:Application>

View source is enabled in the following example.