API integration with WordPress website

Looking someone who can do 2 way API integration with a marketplace website.
Details:
Our website is on wordpress
The marketplace website name is bokun .io
Please read the documentation before making any offer.
This is tour marketplace and we need availability (Calendar available dates , Realtime passengers quantity availability)
After customer book our website send booking data to vendor company.
Flow information:
customer land on our website select date and quantity of passengers (need to take from bokun)
add to cart and put name and contact information and procced to payment.
After payment ( Send booking information Name, and other information to bokun)
Also send a booking voucher to customer.