I'm sure theres many ways to do this but here is what I would do:

Make a control curve next the hand and give it 5 attributes (select curve modify>add attribute) for each finger and you can call them index,thumb,pinky,wedding,middle. you'll see the attributes on the channel box.
then what I recommend is doing driven keys for each finger roll since I assume you just want the fingers to roll in and out in one rotating axis right? so yea just do a driven key for each finger and then you can just click on the index attribute and middle drag and it will move all those joints of that finger very nicely and quickly.

if you need help with setting up the driven keys let me know cause it took me a while to get it at first

This process was very useful for me when I worked on the landing gears of this ship. With the drag of the middle button I had the 50 parts of the landing gear move in and out of its chamber.