1

Run the Runner scheme on your iPhone

Select the Runner scheme and your iPhone, then Run. This installs the Flutter app and the watch app.
2

Install the watch app if it did not install itself

On the phone, open the Watch app → Available Apps → install CarpWatch.
3

Open the watch app once and press Start

watchOS does not run a freshly installed app in the background before its first launch.
4

Grant the permissions

HealthKit, microphone and location prompts all appear on the watch.
From the command line, flutter run builds the Runner scheme and therefore the watch app too: