@scullracer isolating's answer helped me to do so (with flic 1).
I asked flic to open chrome
using the url like described in the article.

I used it without passing on any input.
Just starting the Shortcut

shortcuts://run-shortcut?name=[name]&input=[input]&text=[text]

I replaced [name] with the name of my shortcut and deleted from the first "&" onward.

That helped me to - finally - start the iphone timer.

Thank you @isolating - thank you so much!

Here’s how it works: you can configure your Flic button to simulate a home button press (double or triple clicks). Then, on your iPhone, go to Settings and set a multiple home button press (e.g., double or triple press) to trigger your shortcut.

The downside is that most modern iPhones no longer have a home button. Additionally, the Flic app doesn’t currently offer support for using the triple tap on the back of the phone (a feature available on newer iPhones) as an alternative to the triple click on the home button.

Sorry to hear about the hardware issues. Unfortunately it is not possible to create such action for Flic in iOS due to limitations in the API to trigger arbitrary Shortcuts.