If you are using your own date format, you need to make the validation by your own (custom function). Otherwise, you can use a DateValidator and call validate on DateField change:
<mx:DateValidator id="dateValidator" source="{myDate}" property="text" requiredFieldError="You must choose a date" />
<mx:DateField id="myDate" focusOut="dateValidator.validate()" />
This is a basic example, maybe you will need to tweak it a little. You can also use the reference (it has a working example at the bottom):
http://help.adobe.com/en_US/FlashPlatform/reference/actionscript/3/mx/validators/DateValidator.html