The short answer to the question is "It Can't be Done"—at least not with the existing building blocks of Akka HTTP and the Alkappa Unix Domain Sockets. You would have to handle writing the HTTP GET request by manually sending the headers, i.e. (using the Docker API as an example)
GET /v1.24/containers/json HTTP/1.1\n
Host: localhost\n
\n\n
...and then reading the TCP response manually. Additionally, the Unix Domain Socket logic can't use the Alpakka code because it only currently provides a ServerBinding, and thus is designed to create a server that handles requests to a Unix socket, not to send data to a Unix socket and handle the response.
So everything has to be done manually. There's another StackOverflow question here that points out how the AFUNIXSocket github source code could be used to help with some of the low-level Unix Domain Socket logic that might be of help to others wanting to tackle this same problem.
The most elegant solution would also involve (as suggested by dvim's comment) writing an HTTP.ClientTransport to plug in the Unix Domain Socket communication layer and allow the HTTP library to expose the low-level functionality of writing request/response headers, etc. (One interesting note on that is that the API assumes a host/port parameter pair, which is tightly bound to the TCP paradigm.)