When I put my Apple Watch the Apple logo keep flashing what do that mean

I would suggest you reset your watch. Press the crown and side button in untill the Apple logo appears. Also Check your Watch is updated to 5.3 and your iphone is running ios 12.4.1 Finally Unpair your Watch and repair it. Before any thing full charge your Watch

What red icon? I think one of these links might have what you need to know,

If you see a red "!" on your Apple Watch - Apple Support

If your Apple Watch won't charge or it won't turn on - Apple Support

Reading your first post I suspect a charging issue, or the battery is defective and can’t hold enough power to reboot the watch.