@kerry-thacher Hi!
Unfortunately, no. At least not from what we have found.
You can use the "alternative keymap" in the Universal Keyboard action to prevent the on-screen keyboard from hiding while the Flic is connected, however, this also limits what we can do with keyboard commands.
(Note that you need to "Forget" the Flic from iOS Bluetooth device list if you change the keymap for it to have effect).
So Apple requires the device to identify as a keyboard to be able to do certain things, like trigger system wide keyboard commands (which is what this video suggests as a trigger for Shortcuts), and this enforces the behaviour that the on screen keyboard disappears.
Sorry about this, it would certainly be a neat feature to be able to trigger iOS Shortcuts without affecting the on screen keyboard.