Calculate new date by adding number of days to existing date (excluding weekends and pub holidays)?

Dear Community,

I'm trying to create the following 3 separate fields:
1. Input field that allows selection of an original date in the format DD/MM/YY (ideally using flatpickr, https://flatpickr.js.org/), and _only_ working days (i.e., no weekends or public holidays)
2. Drop-down menu (or otherwise restricted choice field) that allows for a choice of numbers between 1 and 10 inclusive (to indicate number working days)
3. A new date output in the format DD/MM/YY that adds the number of working days (specified in the previous field) to the original date, _excluding_ weekends and public holidays

E.g.,
Original date: 31/07/19
Number of working days: 3
New date: 05/08/19

Does anybody know how I might achieve this in Javascript with flatpickr?