I do not know the service WinHTTP, so I cannot provide an example.
You should investigate RunProgram. It is a JMP function that can run a Windows CMD.exe, VBA, etc.
Attached is a script created for chapter 9 of the book JSL Companion, Applications of the JMP Scripting Language, Second Edition.
By the way, JMP13.2.1 fixes a few issues found in JMP13.0.0.
I hope this script gives you enough to achieve your task.