Tailing the build logs is possible with the kpack log utility.
Downloading the log utility for you operating system from the most recent github release.
To tail logs from all builds for an image
logs -image <image-name>
To tail logs from a specific build on an image
logs -image <image-name> -build <build-number>
To tail logs from an image in a different namespace
logs -image <image-name> -namespace <namespace>
The log utility will not exit when the build finishes.