Does anyone know where to find a map coverage that CenturyLink has for their high-speed internet? I am asking specifically in Colorado.
There is an interactive map from CenturyLink
(from any other source it'll be be hard to find official data)
It references the Mapbox API (and Markers)
Here are two solutions for you, but nothing out of the box. They both require some work to get exactly what you are asking for.
Fixed Broadband Deployment Data from FCC Form 477's
latest iteration is through 2016-06; here is Colorado's: CO Fixed 2016-06
You are going to have to filter out all providers except for Centurylink, and then match the census blocks with a crosswalk so you can map it.