Have you tried using lower-tech devices to help remind him? A paper agenda, Google Calendar, and alarm clocks/wristwatches are all techniques that other autistic people have used with varying levels of success.
If you want to test whether the Echo reminder would help, you should try a lower-fidelity prototype -- record your mother saying the reminder with a tape recorder or a Sound Recorder app on a computer, and then play it back at the appropriate time and see how he responds. (If it was me, I'd find it rather insulting and might respond angrily, but I wouldn't assume your brother acts the same way.)
Does your brother want to live independently of your mother? If your mother is the only social contact that your brother has during the whole day, then replacing her with an Echo might make him even more isolated, right?