UPDATE:
This only seems to work, when my phone is awake and the flic app is on the screen...:-(
@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!