What happens after I drink milk of magnesia to flush my digestive
system? What is removed from my system, the contents of my stomach,
bowel, lower intestine, etc.? How is it possible for the bowels to
actually become dependent on it with repeated use?

Milk of magnesia is a weak base compound.  When comsumed, it acts in
the same way as adding baking soda to vinegar, neutralizing excessive
stomach acid that causes heartburn and acid reflux. When the reaction
thats place it creates a salt and water, just as all acid-base
reactions do.  Excessive use could hinder the digestion of food that
occurs in the stomach at the time of consumption.  It will have little
effect to the digestion or operation of small and large intestines. 
Whether or not you can become dependent of milk of magnesia is a tough
question to answer.  Should you feel dependent upon it, more then
likely you are producing too much stomach acid or perhaps have a
stomach ulser and should consult a physician for treatment.

First: If you have questions about medicines that you are actually
taking, you should go to your doctor for evaluation and treatment.

Bman04-ga: as my mother-in-law is fond of saying: true, but lacking in
interest.  The question is how MOM has a laxative effect ("flush my
digestive
system"), and how it is possible to become dependent on it.

1)  MOM (magnesium hydroxide) has 2 methods of action.  First is
osmosis.  Because the magnesium ion is not absorbed through the walls
of the gut, it causes water to enter the lumen of the gut, which then
essentially washes the contents of the gut downstream, resulting in a
watery bowel movement.  Secondly, magnesium (through an unknown
mechanism) causes the release of a hormone that increases the water
and electrolyte content of the small bowel, again increasing transit. 
(source: micromedix.com, quote: "A. MECHANISM OF ACTION
1. Saline laxatives have an osmotic effect causing increased
intraluminal volume which acts as a stimulus for intestinal motility.
Laxatives that contain magnesium have been shown to release
cholecystokinin which causes intraluminal accumulation of fluid and
electrolyte and promotes small bowel and possibly even colonic transit
(Tedesco et al, 1985; Pietrusko, 1977). "

2.Dependence on laxatives usually occurs with motility agents that act
directly on the bowel wall.  But this can occur with MOM as well, as
motility is increased by the increase volume of the colon, as
mentioned above.  Basically, your body gets used to having an
increased volume of crap in your colon, and when you stop using MOM,
you get constipated.  Incidently, the side effects of chronic use of
MOM can be MUCH MUCH worse than simple habituation.  Also from
micromedix.com  "LAXATIVE ABUSE
1. Typical symptoms of LAXATIVE ABUSE include abdominal pain,
weakness, fatigue, thirst, vomiting, edema, bone pain (due to
osteomalacia), fluid and electrolyte imbalance, hypoalbuminemia (due
to protein-losing gastroenteropathy), and syndromes that mimic colitis
(Longe & DiPiro, 1992). If the bowel has not been permanently damaged,
it may require several months to retain the bowel without the
assistance of laxatives (Curry & Tatum-Butler, 1993"

If you have questions about medicines that you are actually taking,
you should go to your doctor for evaluation and treatment.