The light flashes all the time even there is no call on the answer machine.

SOURCE: Message Light flashing continously

Resetting the New Message LED
If the LED remains on after you’ve retrieved your messages, you may need to reset
the indicators. With the phone is in standby mode, press and hold find handset on
the base until the paging sound stops (about 5 seconds).

SOURCE: The flashing light on phone

Press down the "find handset" button until the paging beep stops (about 5 seconds) and this will reset the indicator lights on the handsets.

SOURCE: voicemail light is flashing. How do I get message?

If you have a voice mail box set up, and you don't use your answering machine for messages, that would be something that is set up through your phone company (AT&T, Verizon, etc.).

Typically, to access your voicemail, you would dial your home phone number, and then when your message picks up (either the automated message or your personal greeting) press the asterisk or star key (*) and then enter your password. Depending on your particular voicemail, you may have to hit the pound key (#) after your password as well. Then, once you are logged in, the system should tell you whether or not you have any new messages, and if you do, generally you would press "1" to hear them.

Hope that helps! If you can't get in to your voice mail or your password doesn't work, you would have to contact your local phone service provider for assistance.

SOURCE: My answering machine light is blinking on my

If you also have voice messaging with your phone company, you might have voice messages stored with them. If so you need to access it with your password to clear them. To find out if you do have voice messaging, call your phone company and they can let you know and reset your password if so.