Robert,
Yes, you absolutely can shine a flashlight through it, in fact this has become one of my favorite hobbies!
At first, when you look through from the other side, you will just see a diffuse red glow or maybe nothing at all. Over time (say a week or so), the red glow will become brighter and more focused. Eventually you will be able to see the lens of the flashlight very clearly. It will be very dark red, but it should not look fuzzy once it's done clearing.
Start at the top of the carboy and then slide the flashlight and your head down, and you should see the wine gets darker/cloudier as you slide down. When it's nice a clear all the way from top to bottom, then it's done clearing.
I just bottled the Grenach/Shiraz/Mourvedra which is a very similar wine kit, and it took about two weeks longer than the instructions said. So I racked after 8 days as instructed, then it took about 24 more days to be nice and clear not the 14 days the instructions called for. I didn't do anything extra, I just gave it more time.
Good luck!