There may be a few things that could keep your Slingbox from connecting to your Chromecast. First you should check that you have a model that is supported for use with your Chromecast. I've included an article below that should help you find out that information.
Next you'll want to make sure your router is port forwarded. Chromecasts require TCP, which is a top streaming protocol to be active on your router. This basically tells your router to let the Slingbox through to your Chromecast, which is why it may work on other devices, but not the router. The article below should give you more information on what it is and how to do it as well as more information on Chromecasts.
- Slingbox.com - What's port forwarding/port mapping?
- Slingbox.com - Frequently asked questions about SlingPlayer for Chromecast
I hope that helps!
Sling Media Technical Support