If you found out your Leader or Immediate Supervisor was doing something against the law, like fraud, what would you do?

As long as you have enough rank for someone to actually care it might go somewhere. It may depend on the infraction but so far it’s always had to wait until an E-8 or officer notices.
Unfortunately in guard world we do have things that happen like this and if you’re not an NCO reporting it won’t do anything except getting you chewed out. We have had people drunk on duty before, officers and NCOs alike, and it really doesn’t matter how many E-4s and below go report it even with video and a vehicle accident. Gets swept under the rug in some units.

This happened to my brother in Vietnam. A officer in my brothers command was writing off weapons' as damaged beyond repair or lost in combat operations. In actuality the weapons' were fine and he was sending them to a civilian contractor in Saigon who would ship them to the United States then sell them at a huge profit. My brother E-5 reported it to the captain 0-3. As the thief was a 0-5 LT col with 22 years he had to go to the COL 0-6. The Col told the LT Col to put in his papers to retire and nothing else would be done. The 0-5 Was well protected as he was a ring knocker from West point. He also had friends with high political power who could block the COL pending promotion to 0-7. So the COL let him slide and he was promoted 2 months later to General. The LT col retired and was given a retirement medal from the COL for his outstanding work.

Got to pick your battles carefully

tell the MP'S

Unfortunately this does happen quite often in our military but also out in the real world. I’ve been on many JAGs and I can’t tell you how many were just plain stupidity and no common sense. I remember after firing on the Rifle Range at Camp Hanson, just before I was ready to turn my weapon into the Armory, a terrible accident happened. An innocent Marine Armorer and a couple of Marines were seriously injured. Unfortunately the young Marine didn’t survive and another Marine Officer. If it happened on my watch I would definitely go up the Chain of Comand.

Stay silent. Unless I was ready to suffer consequences

I was once ordered to complete the advancement courses for one of my enlisted who had not done them (COs were graded at the time by advancement percentages). I asked the CO (an O-5) to put that in writing. After a moment, he revised his order to "do whatever it takes to insure his courses are turned in". I had to spend a weekend with him asking the questions one-by-one, then having him look up the answers (he knew almost none of them), then mark down the answers. Courses completed, but he failed the advancement exam. CO not happy with me!
A couple of years later he was caught (as an O-6) during a field exercise for numerous violations and bad judgement decisions (staying in hotels nightly with his family vs. in the field with the unit; private transit to field with family in personal car vs. convoy with unit; etc.). Went to Flag Mast; relieved and retired immediately. Should have been more.

I figure if I found out about it others can/will also and if they turn him/her in then there will be an investigation and if it is found out I knew and did not turn him/her in then I am in trouble too. So I am going to be the one doing the turning in to protect myself. May sound selfish but that is the way life works.

Turn their sorry behinds in.

Without going into details, I believe any officer who is engaged with his command, will become aware of issues that could be problematic to the integrity of the unit. I will also state that when in combat the level of discretionary authority can be much broader. For example, the "acquisition" of vital materials "may" require diversion from more "established" chains. This action, although subject to official sanctions, is not intended for personal gain, profit or illegal "enterprise" but is taken to support the men who will and are performing a vital mission.

Although claiming deniability by remaining ignorant (or claiming ignorance) may be an answer to senior command upon discovery of the "diversion", a true leader will, 1) either stop or prevent such actions, or 2) stand responsible for the actions of the men under your command. There is no middle ground and a true leader will not leave his men to hang for actions he was aware of and supported, either by commission or omission.

Integrity is something that cannot be taken from you; you are the only one who can give it up. Once lost, it is nearly impossible to gain it back.

There is a difference in circumventing red tape for the mission and compromising integrity so someone can profit with personal gain. By turning a blind eye to this - by not performing your constitutional oath of office - you enter into a symbiotic relationship. A relationship of condoning the illegal action(s) by commission or omission. Eddie Rickenbacker stated "Courage is doing what you are afraid to do. There can be no courage unless you are scared." Ultimately, someone will know what you did and what you decided. Not everyone will support you regardless of your decision. This is why you have been chosen for the command position you hold.