What are you using to view the video stream? Have you encountered a problem viewing?
I don't think you need to worry about this - the Slingbox regularly reports it's IP address to your sling account held on the sling servers, so whenever you go to view the stream it first looks up your account and then gets the current IP address.
That's the first thing resembling a helpful answer I"ve heard since I first put this question to two different Sling tech folks, each of whom reacted to me like I had spiders crawling out my years.
So, what I'm understanding is that as a matter of its operation, the Slingbox determines the public-facing IP address of its WAN and sends that along with its internal finder ID to Sling, so Sling always knows the proper IP address. That precludes the need for an externally maintained IP address (via Dynamic DNS).