You can scroll the Flex TextArea control vertically using the verticalScrollPosition and maxVerticalScrollPosition properties, as seen in the following example:

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

    <mx:Script>
        <![CDATA[
            private function init():void {
                callLater(setMaxVScrollPos);
            }

            private function setMaxVScrollPos():void {
                slider.maximum = textArea.maxVerticalScrollPosition;
            }
        ]]>
    </mx:Script>

    <mx:String id="lorem" source="lorem.html" />

    <mx:ApplicationControlBar dock="true">
        <mx:Form styleName="plain">
            <mx:FormItem label="verticalScrollPosition:">
                <mx:HSlider id="slider"
                        minimum="0"
                        snapInterval="1"
                        liveDragging="true" />
            </mx:FormItem>
        </mx:Form>
    </mx:ApplicationControlBar>

    <mx:TextArea id="textArea"
            text="{lorem}"
            verticalScrollPosition="{slider.value}"
            verticalScrollPolicy="on"
            width="100%"
            height="100%"
            resize="init();" />

</mx:Application>

Peter

In the example above, select the checkbox and try scrolling the TextArea control’s vertical scrollbar thumb. As you click and drag the scrollbar thumb, you should see the text scroll line by line.
Now, deselect the checkbox and try again. Now the text doesn’t scroll as you drag the scrollbar, but will scroll to the correct position when you release the scrollbar thumb.

Peter