I looked in your log file. It looks like you are compiling the library and picking up an incompatible version of already-compiled TinyCLR or at least mscorlib. Your nuget config might be pointing at TinyCLR files that you downloaded, or your bin and obj dirs may be poisoned with a .net framework version of mscorlib.
First, make sure that the packages dir at the root of your enlistment is empty. Then do a ‘clean’ on the solution. We need to make sure that you don’t have another copy of mscorlib lurking around.
Then, make sure that nuget.org is the only enabled Package source because you may be picking up a conflicting copy from there:
Solution -> Right click -> Manage nuget, then click on the gear in the upper right corner of the nuget window. Make sure that only nuget.org is checked:
The nuget config is a global setting - you will have to change it again when compiling other projects. You can see that I also have an x:\nugetrepo\tinyclr dir where I put my compiled nuget packages from the library build, and I check that when compiling projects that consume the lib that I built locally. I populate that dir by running this command from the root of the TinyCLR Library source dir:
FOR /F "TOKENS=*" %f in ('DIR /B /S *.nupkg') do copy /y "%~f" "x:\nugetrepo\tinyclr"
I AM able to compile TinyCLR Libraries with both nuget.org and my local build selected, and generally I just leave it set that way. I unchecked it here for illustration. Your problem may be arising because you are also pointing at a downloaded copy. Just guessing here as I haven’t hit this particular problem.