My Apple Watch is flashing blinking an Apple logo while charging

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 > https://support.apple.com/en-us/HT201232