UPDATE: This was a fun experiment, but I strongly suggest lsp-mode, which works incredibly well with typescript. I wished I had discovered this earlier:
https://emacs-lsp.github.io/lsp-mode/page/lsp-typescript/
This is a very basic flymake backend for typescript. It will find the tsc executable in the current project.
While working on a small 3D game for fun with BabylonJS, I realized there was no typescript-flymake package. I wasted a whole saturday coding this.
Currently, it is not configurable (as in we can't change the command executable). Also, we cannot set a config. Also, the package is not on melpa/elpa yet.
Any help is welcome, from documenting, finding bugs to addressing shortcomings!