I do not seem to be able to create a flow that when I push the button it will call some URL with certain parameters. Does that exist?

Yes - add the 'Maker' thing - it will send HTTP GET/POST/PUT.

Or Triggi (www.triggi.com) . Direct competitor to Stringify from the NL. Disclaimer: I work there as Creative Technologist

is there going to be a web version?

Android first, then we'll look at web.