<mx:GridLines direction="both"
    horizontalTickAligned="false"
    verticalTickAligned="false">

    ...

</mx:GridLines>

Full code after the jump.

View MXML

<?xml version="1.0"?>
<!-- http://blog.flexexamples.com/2007/11/19/aligning-data-in-a-flex-linechart-control-to-horizontal-and-vertical-tick-marks/ -->
<mx:Application xmlns:mx="http://www.adobe.com/2006/mxml"
        layout="vertical"
        verticalAlign="middle"
        backgroundColor="white">

    <mx:Script>
        <![CDATA[
            import mx.charts.CategoryAxis;
            import mx.charts.chartClasses.IAxis;

            private function linearAxis_labelFunc(item:Object, prevValue:Object, axis:IAxis):String {
                return currFormatter.format(item);
            }

            private function categoryAxis_labelFunc(item:Object, prevValue:Object, axis:CategoryAxis, categoryItem:Object):String {
                var datNum:Number = Date.parse(item);
                var tempDate:Date = new Date(datNum);
                return tempDate.date.toString();
            }
        ]]>
    </mx:Script>

    <mx:CurrencyFormatter id="currFormatter" precision="2" />

    <mx:XMLListCollection id="dp">
        <mx:source>
            <mx:XMLList>
                <quote date="8/1/2007" open="40.29" close="39.58" />
                <quote date="8/2/2007" open="39.4" close="39.52" />
                <quote date="8/3/2007" open="39.47" close="38.75" />
                <quote date="8/6/2007" open="38.71" close="39.38" />
                <quote date="8/7/2007" open="39.08" close="39.42" />
                <quote date="8/8/2007" open="39.61" close="40.23" />
                <quote date="8/9/2007" open="39.9" close="40.75" />
                <quote date="8/10/2007" open="41.3" close="41.06" />
                <quote date="8/13/2007" open="41" close="40.83" />
                <quote date="8/14/2007" open="41.01" close="40.41" />
                <quote date="8/15/2007" open="40.22" close="40.18" />
                <quote date="8/16/2007" open="39.83" close="39.96" />
                <quote date="8/17/2007" open="40.18" close="40.32" />
                <quote date="8/20/2007" open="40.55" close="40.74" />
                <quote date="8/21/2007" open="40.41" close="40.13" />
                <quote date="8/22/2007" open="40.4" close="40.77" />
                <quote date="8/23/2007" open="40.82" close="40.6" />
                <quote date="8/24/2007" open="40.5" close="40.41" />
                <quote date="8/27/2007" open="40.38" close="40.81" />
            </mx:XMLList>
        </mx:source>
    </mx:XMLListCollection>

    <mx:ApplicationControlBar dock="true">
        <mx:Form styleName="plain">
            <mx:FormItem label="direction:">
                <mx:ComboBox id="comboBox">
                    <mx:dataProvider>
                        <mx:Array>
                            <mx:Object label="both" />
                            <mx:Object label="horizontal" />
                            <mx:Object label="vertical" />
                        </mx:Array>
                    </mx:dataProvider>
                </mx:ComboBox>
            </mx:FormItem>
            <mx:FormItem label="horizontalTickAligned:">
                <mx:CheckBox id="hCheckBox" selected="true" />
            </mx:FormItem>
            <mx:FormItem label="verticalTickAligned:">
                <mx:CheckBox id="vCheckBox" selected="true" />
            </mx:FormItem>
        </mx:Form>
    </mx:ApplicationControlBar>

    <mx:LineChart id="lineChart"
            showDataTips="true"
            dataProvider="{dp}"
            width="100%"
            height="100%">

        <!-- background elements -->
        <mx:backgroundElements>
            <mx:GridLines direction="{comboBox.selectedItem.label}"
                    horizontalTickAligned="{hCheckBox.selected}"
                    verticalTickAligned="{vCheckBox.selected}">
                <mx:horizontalFill>
                    <mx:SolidColor color="haloBlue" alpha="0.2" />
                </mx:horizontalFill>
                <mx:horizontalAlternateFill>
                    <mx:SolidColor color="haloSilver" alpha="0.2" />
                </mx:horizontalAlternateFill>
                <mx:verticalFill>
                    <mx:SolidColor color="haloBlue" alpha="0.2" />
                </mx:verticalFill>
                <mx:verticalAlternateFill>
                    <mx:SolidColor color="haloSilver" alpha="0.2" />
                </mx:verticalAlternateFill>
            </mx:GridLines>
        </mx:backgroundElements>

        <!-- vertical axis -->
        <mx:verticalAxis>
            <mx:LinearAxis baseAtZero="false"
                    title="Price"
                    labelFunction="linearAxis_labelFunc" />
        </mx:verticalAxis>

        <!-- horizontal axis -->
        <mx:horizontalAxis>
            <mx:CategoryAxis id="ca"
                    categoryField="@date"
                    title="August 2007"
                    labelFunction="categoryAxis_labelFunc" />
        </mx:horizontalAxis>

        <!-- horizontal axis renderer -->
        <mx:horizontalAxisRenderers>
            <mx:AxisRenderer axis="{ca}" canDropLabels="true" />
        </mx:horizontalAxisRenderers>

        <!-- series -->
        <mx:series>
            <mx:LineSeries yField="@open" displayName="Open" />
            <mx:LineSeries yField="@close" displayName="Close" />
        </mx:series>

        <!-- series filters -->
        <mx:seriesFilters>
            <mx:Array />
        </mx:seriesFilters>
    </mx:LineChart>

</mx:Application>

View source is enabled in the following example.