Hey,
Found this at (techwalla)
Getting your unit to stop flashing its message light is pretty simple: Listen to the messages. From the base of the unit, you can typically do this by pressing the "Play" button and then listening to the messages. From your cordless phone, you'll typically press the envelope icon. The system will play the new messages first, followed by any saved messages. Once you've listened to all of the new messages, the lights on the base unit and the cordless phone should turn off. Since every Uniden cordless phone system is slightly different, check your unit's user guide for more specific instructions on playing, deleting and saving messages.
Not sure if it will work for this model, if not then you can go to this manuals site for the 1715 - you should be able to identify the model from that.
https://www.manua.ls/uniden/dect-1715/manual
Hope this helps