My fish is sick and just lying on the bottom of his plastic bowl.
My mom wants me to flush him but I dn't want to unless he is dead.
How do you tell if a fish is dead?

apart from not moving does your fish have any other signs of not being well? as oranda said, could just be stressed

I tried feeding him some peas but he wouldn't eat them.

Sorry to hear from your loss.

But before you get a new fish:
  1.Do you know that goldfish should NOT be kept in a bowl?
  2.They need at least 10 gallon per fish to be happy.
  3.They need good filtration and aeration.
  4.They need perfect water quality.
  5.A partial waterchange has to be done EVERY week, about 15-20%
  6.The water parameters MUST be checked on a regular basis. Those are Ammonia, Nitrite, Nitrate and pH.
  7. Before you put fresh water in, you should use a conditioner to remove chemicals from the tap water        and you also should adjust the pH to about 7.2-7.6

If you do not provide all this, the fish will be stressed out. Stress leads to bacterial and fungal infections >>> abnormal behaviour >>> death.  Sure you don't want this to happen again and have another poor fish suffering. Remember, they are living creatures and do feel joy, happiness or pain like we do.

If you cannot get a proper tank and equipment for a goldfish, you better get a Betta instead

Thanks Nossie, you and Andrea too, for supporting