TSLint in Visual Studio 2015/2017?

This is reported as an issue in the Visual Studio Developer Community. https://developercommunity.visualstudio.com/content/problem/22907/please-support-tslint-as-how-its-supported-in-vs-c.html

The status is "triaged", so I assume that a comparable feature is not (yet) available. You may want to upvote the issue, so that it gets more attention by the VS development team.

EDIT: As noted in the following question, the visual studio plugin web analyzer provides support for tslint in VS 2015 (but not VS 2017):

Set up TSLint for VS2017

As @Hermann Gruber has mentioned, in Visual Studio 2015 Mads Kristensen's Web Analyzer extension provides support for TSLint of the kind you require.

For Visual Studio 2017 and 2019 I have now personally upgraded Mads' extension, and rebranded it as 'TypeScript Analyzer' as it only supports TSLint. It's available in Visual Studio's Extensions and Updates Gallery under 'TypeScript Analyzer'.

This is something I coded in a day or two (note that I haven't worked with C# for a few years):

https://github.com/vladeck/TSLint

It is a start of (hopefully) worth-wile Visual Studio 2017 extension that can mark .ts code withing the editor, based on the installed tslint and tslint.json configuration.

It is not published on the marketplace yet (a lot more coding to do), but you can download and build it yourself. Give it a try, If you have the time. The more people try it out, the more I will have data needed to make it worth-wile.