I am using python3.7 on Windows 10 operating system. I had same issue and after a long research I had installed it successfully.
Install “Microsoft Visual C++ Build Tools” AND My OS is having 64 bit operating system but still then it need to install 32 bit version “mysqlclient‑1.4.2‑cp37‑cp37m‑win32.whl”
Download binary wheels from “https://www.lfd.uci.edu/~gohlke/pythonlibs/” and run command
pip install [path_to_downloaded_file] eg: C:\Users\Ds\mysqlclient-1.4.2-cp37-cp37m-win32.whl
use pipenv instead of pip if you are using virtual environment.