We have the following SDKs for computers:
https://github.com/50ButtonsEach/fliclib-linux-hci
https://github.com/50ButtonsEach/flic-service-osx
https://github.com/50ButtonsEach/fliclib-windows
For Macintosh we also have a user-friendly app: https://github.com/50ButtonsEach/hax-with-flic-osx.
For the Mac app the user must configure it, I'm not sure how easy it is.
For the SDK/daemon variant, the solution is that we have a daemon executable running that implements a TCP server. Then we have client libraries for a couple of languages you can use to connect to the server. Usually the server runs at localhost so you can only connect to it from the same computer. You would need to implement a client application that connects to the server, implements the pairing process in a user-friendly way and listens to Flic button events. When you receive an event, you can start a browser process with the web page URL as program argument.
The user need to download both the Flic daemon and your application (you can bundle it in one zip file for example, or even make an installer). Without the software, it will be impossible to connect the button to the computer (or technically yes through some system Bluetooth settings maybe but that won't be much use since there is no software that can interact with it).