Unplug it. Wait 5 minutes and plug it back in.
Do not plug it in when there is a battery in it.
Plug it in first, then put the battery in.
Do you have a meter? Check the output. It should be 4.2V.
If the output is correct, put a battery in and see if the red light changes to steady red.
Then, take the battery out and see if it changes to green.
The idea is to reset it.
If this is a TR-001, the light should be steady green if the battery bay is empty.
When you put the battery in, it should turn red until the battery is charged, then it turns green.
If you can't get it to stop blinking, you will need to return it.
If it is putting out 4.2V, you could charge a battery on it, but you will need to be very careful and check the battery voltage often so that it doesn't overcharge. If you're lucky, it'll turn green when it's done (at 4.2V), or it will stop blinking red while it's charging.
I have a small charger that does the same thing. it blinks red, but it turns to solid green when the
batteries are charged. I don't think it's supposed to blink, but it doesn't seem to be affecting the way it works.