Apple watch logo flashing

flashing, spinning or steady  logo 

If the Apple Watch has stopped responding,I suggest performing a forced restart. Steps needed are found in the Apple Support article: Restart your Apple Watch - Apple Support 

i.e. press and hold both the side button and Digital Crown for at least 10 seconds, then release both buttons when you see the Apple logo. 

If you've completed that troubleshooting and the issue is still not resolved, Contact Support. 

Click here > Contact - Official Apple Support  or phone numbers Click here > Contact Apple for support and service - Apple Support and or Genius Bar Reservation and Apple Support Options - Apple

While LD's offered excellent advice, please remember this watch is at least 8 years old or so, and there's a good chance its battery is kaput.

Good point and batteries are not available for series 1 and so Apple would recommend a new Watch.