Your solution file as it currently exists in your GitHub repository does not contain any project information as the error suggests. I downloaded a copy of your repo and opened the solution in Visual Studio 2015 and it did not have any projects associated with it.
https://github.com/AndrewShepherd/kudu-deployment-test/blob/master/kudu-deployment-test.sln
Microsoft Visual Studio Solution File, Format Version 12.00
VisualStudioVersion = 14.0.25420.1
MinimumVisualStudioVersion = 10.0.40219.1
Global
GlobalSection(SolutionProperties) = preSolution
HideSolutionNode = FALSE
EndGlobalSection
EndGlobal
Once I added the existing project from the files in the repository, this is what my updated solution file looked like:
Microsoft Visual Studio Solution File, Format Version 12.00
VisualStudioVersion = 14.0.25420.1
MinimumVisualStudioVersion = 10.0.40219.1
Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "kudu-deployment-test", "kudu-deployment-test\kudu-deployment-test.csproj", "{AA0F0FD5-559E-4125-87A7-F7C3173DE079}"
EndProject
Global
GlobalSection(SolutionConfigurationPlatforms) = preSolution
Debug|Any CPU = Debug|Any CPU
Release|Any CPU = Release|Any CPU
EndGlobalSection
GlobalSection(ProjectConfigurationPlatforms) = postSolution
{AA0F0FD5-559E-4125-87A7-F7C3173DE079}.Debug|Any CPU.ActiveCfg = Debug|Any CPU
{AA0F0FD5-559E-4125-87A7-F7C3173DE079}.Debug|Any CPU.Build.0 = Debug|Any CPU
{AA0F0FD5-559E-4125-87A7-F7C3173DE079}.Release|Any CPU.ActiveCfg = Release|Any CPU
{AA0F0FD5-559E-4125-87A7-F7C3173DE079}.Release|Any CPU.Build.0 = Release|Any CPU
EndGlobalSection
GlobalSection(SolutionProperties) = preSolution
HideSolutionNode = FALSE
EndGlobalSection
EndGlobal
If your project is correctly visible in Visual Studio, I would make sure that your solution file is saved and the updated version is pushed to your repo. Since you have already setup continuous deployment from GitHub, once you fix the solution file, your project should automatically deploy correctly.