I met with a screen reader user who had mentioned a great example of accessible date form control:

Greyhound Canada has a accessible date picker control which allows screen reader user to edit the date with up and down arrow keys and also navigate using the pop-up calendar.

There is also an accessible Bootstrap date picker available: ab-datepicker This date picker can be customized and has great accessible features when I put it to test with NVDA screen reader. When user navigate to the pop-up calendar it announces with detailed description about the calendar picker. If you are looking to add a accessible date picker to your page, this one is worth checking out for.