This is something that is easy to achieve without jQuery, or flash.
JavaScript alone could do it. (html alone would be too messy)
When clicked, use JS to switch the image (if showing front, change the source to the image for the back of the card else change the source to the image for the front).
If desirable, you could alternatively use the mouseover and mouseout events to show the front and back of the cards without any clicking necessary. Fully working example follows (assuming image names are correct!).
HTML Code:
<img src="card1_front.png" alt="Card 1"
onmouseover="src='card1_back.png'" onmouseout="src='card1_front.png'">
If you want a fancy card-turning over effect as a transition, consider making the card images animated, without a loop. Simple!