It's a great run. My spouse and I do it every morning at CSA. If you are facing the ocean, you can run to the right past Beaches, and and then do a little "trail running" and that takes you past Sandals and up to the point where Hedo starts. That's about 2 miles each way.
If you head to the left, you can run all the way down to a public beach. It's also about 2-ish miles.
The slope all depends on the tides. If the tide is out, it's a nice flat run in both directions. If the tide is IN, it's a little sloped and you might get your shoes wet in a couple of spots. Regardless, it's a great run, and the people you'll see along the way are really nice.
I'm very much looking forward to running along the beach. I even considered bringing an extra pair of shoes, but decided that was going a little overboard. I've been running for about 1.5 years now, but never along a beach. That's even worth getting up early to experience!
Indeed, if you are a running enthusiast then running the beach is not to be missed. I usually make the left turn at the beach and head south. Lots of Jamaican culture to take in, several smaller resorts and many bars and restaurants to pass by. Definitely run in the morning, soon after sunrise. The beach will be mostly unoccupied and makes running easier, not to mention that it gets quite hot very early in Jamaica. Run just above the water line where the sand is fairly firm and footing is good. You will get the hang of it quickly. Your feet will most likely get wet, I have never made a run without stepping in the water at some point. So wear appropriate foot gear. Some like to run barefoot even, but that is not my style for much more than a short jog.