The watch doesn’t need to be connected to the bike itself. The Flow app could record the data directly from the watch HRM or take it from the Health app.
I’ve just been out for a ride and had the Heart rate monitoring setup. The Flow app is now on my Apple Watch and displays my heart rate in real time during the ride. However, none of the heart rate data appears to be recorded by the Flow app &/or transferred to Strava at the end of the ride.
You can allow the Flow app to read heart rate data from your Apple Watch, as follows: Flow App > Settings > Connected Services > under 'Available apps' select 'Apple Watch Heart rate Data'.