Well, what I've been doing with my DirecTV DVR is I listen to the radio broadcast on iHeartradio through my phone/headphones, then I pause the DVR of the game until it lines up with the radio call. Since the stream through iHeartradio is behind by a minute and a half or so, it lets me sync them up nicely. I would think your Sling TV has DVR/pause capability but guess I'm not sure.
It's awesome now that Learfield allows the radio broadcast to be streamed. I suppose if your Sling TV has a longer delay than iHeartradio you're screwed, but it's worth a shot.