How to let users record video via webcam and then upload the recorded video to the site all through the browser using flash player and php in the backend

There's nothing built into Adobe programs that can do what you're looking for. To develop something like this, and do it securely, a programmer would need to fully understand html, css, javascript and php (being relatively skilled in the last one) and ultimately they could use DW to code the site manually. There are some paid extensions that would make writing connection scripts to a database easier in Dreamweaver, but that's all the help Adobe programs will give, aside from a few design templates.

The main thing you're going to need to do is become intimately familiar with security measures on your server and within php. You don't want some random person creating an account only to upload a virus, or download user information because security holes were left open.

The use of Flash content isn't going to work either. Currently, mobile devices don't have the ability to see Flash, the same devices most people will use to record video (webcams aren't nearly as ubiquitous as smartphones with video recording capabilities) and Adobe is set to completely discontinue the Flash plug-in all together in 2020. It's a "dead technology walking" on the web.