There are two primary arguments for a flat tax, simplification and removing the disincentives for productivity. There are also a couple of ways to go about a flat tax. But before we try to simplify the tax code, we must first look at why it is so complex.
Part of the reason that the system is so complex is that there have been too many cooks in the kitchen. As senators, representatives, and presidents come and go, they all try to add or subtract this thing or another for this reason or that and things get very complicated very quickly. This sort of complication for the sake of complication is very easy to dismiss, but some of the complication actually serves a purpose.
For example, there are many tax breaks given to people who own real estate. This is designed to encourage affordable housing. This gives an incentive for a person who has the cash to by an extra house to buy it and rent it to someone without the ability to buy a house. So the major benefit for owning property is a tax one not a profit one. If landlords were only after profit, there would be a lot less of them, rents would be higher and homeless rates would be higher.
Another example is that the lowest income brackets don't actually pay income tax. There are actually situations where you can get a tax refund greater than the amount you withheld. This is designed around the theory that if a person doesn't make enough to live on, any you take a portion of it away from them, you further increase the odds that the state will have to pay for them through a welfare program. In this case it is more cost effective to just let them keep their money rather than take it away and then give it back.
Suffice to say a flat tax is not a perfect system and their will be trade offs.
Now there are two ways to go about a flat tax. Flat income tax, or flat sales tax. What most people talk about with a flat tax is a flat income tax because it prevents international companies to do business in the US without paying taxes. I will focus on this because it is the more realistic of the two. Some may do a federal income and leave sales taxes for the state.
The major problem with our current system is that there is a disincentive for productivity. For example, if you own a business, and it takes 2 man hours and $20 worth of supplies to produce and sell a $100 product. If you are paying someone $10/hour to do the work your net profit is $60. If the government takes 20% you actually come home with $48. As you become successful, the Government (state, federal, local etc) can take up to 55% of that profit meaning that you take home $27 for each product you produce.
So at some point, every company has to look at diminishing returns. Is it really worth their while to hold and administer all the employees that are needed to produce a product. Is building a larger facility worth the investment? On some levels, profit is profit, but in other situations businesses may decide that the work is worth it to earn $48 but not worth it to earn $27.
Another consideration is that the person earning $10 an hour is more likely to get a raise if he is generating $24/hor for his boss than if he is generating $13.50/ hour for his boss.
So we see that in a flat tax both employer and employee are likely to take home more money, but what about government income? This is a situation of mutual benefit. If the business has an incentive to produce more and earn more this will lead to greater profit and in turn greater income tax payment. The employee will also be earning more and pay a greater tax amount.
Now who would this flat tax hurt? Where a flat tax would hurt the most is that there are a lot of "tax professionals" who would be out of business. Huge numbers of government employees who's jobs are primarily to sift through tax returns would be out of work. This would make the government more efficient, and allow more of our tax dollars to be used for something useful, but would cost jobs.
The flat tax would also hurt those who don't pay taxes. Those people who earn income but don't earn enough to pay taxes would under the new system have to pay taxes. People will have any number of opinions on this, but you will find that most people who pay taxes think everyone should pay them, and most people who don't will be screaming foul. Just remember that if we get to the point, where there are more people who don't pay taxes than do pay taxes, and they can vote themselves government benefits from the cash supplied by those who do pay taxes, our society is doomed. So it is not a bad idea for everyone to pay at least something.
In the end, this is not as cut and dry as many will have you believe, but the benefits outweigh the costs. In the end it will create a more efficient and cost effective government, and a more productive nation.