I question whether you actually need a stomach cleanse, unless you have worms in there (which is a different matter), but if you do need a stomach cleanse a fast on juice would get your stomach clean within a day or two, I would say.
Also not eating again until your stomach is empty will help.
It's more likely your issue is with the duodenum, jejunum and upper illeum, if not the entire tube (big and small intestines). It could also be related to gallbladder/liver issues. It would be worth trying a good bowel cleansing program and then some dietary improvements to see the effect this would have on your possible stomach problem. My guess is it would improve drastically.
Are you taking a probiotic of any kind? This could also help. As would digestive enzymes in supplement form.
Another thing to consider is your posture (especially while eating), and if you need any chiropractic adjustments, or strengthening of core muscles, which help to hold all your organs in place. Sagging, squashed organs don't work at their best.
Also, are you eating in a peaceful atmosphere? And do you do anything to relieve stress in your life?