I've seen some custom settings files used in combination with TFS build, but nothing native. Does Team Foundation Server or Visual Studio Team Services have a Jenkinsfile-like, declarative method for defining a build process?
The strict answer is no, in that there is no direct equivalent to a
Jenkinsfile. However, there are Build Process Templates and you can use the Psake Build Automation tool in combination with templates to reduce the barriers to entry for creating a new build, test and deployment build definitions.
It is nowhere near as fluid as Jenkins' Pipelines as Code, AppVeyor's
circleci.yml and Travis'
.travis.yml. There is a wealth of information on the ALM Rangers Library of tooling and guidance solutions.
Visual Studio Team Services has a YAML Build feature in public preview that allows you to store your build definitions as source controlled files.