There’s a discussion on the BBC site about the merits of flat tax, as idea that the Adam Smith Institute proposed for the UK in 2004. Several good points in favour of it are made by Rory Meakin of the Taxpayers’ Alliance. Its chief virtue is that it cuts complexity. In place of our 17,000 pages of tax code, one of the world’s longest, would be a few simple rules. In place of the various different rates, thresholds and exemptions, there would be a simple tax rate for all incomes earned above the minimum wage. This might be 22% or 25%, but would be substantially lower than the top rates currently in force.
There would be two principal effects. The simple low rate would reduce the incentive for both legal avoidance and illegal evasion. It would be easier just to pay the tax. The tax base would thus be broadened as more income became taxable. The second effect would be economic expansion as business activity became more worthwhile. There would be rapid growth, and a further broadening of the tax base from the increased economic activity. This would enable the low flat rate to raise sufficient revenue to fund services.
The arguments against are misconceived. The rich would pay a lower rate, but they would pay more tax, and a higher proportion of the total tax take. Low earners would not pay more because the raised threshold would remove those on or below the minimum wage from income tax altogether. Much of the tax code could indeed be eliminated because with low flat taxes business would not need all the exemptions and allowances. Only tax accountants and revenue officers’ unions would stand to lose.
There is one other virtue of a flat tax. Some people support high spending programmes if they think that someone else will be paying for them. With a flat tax it is clear that everyone would pay for them, and people would be less receptive to politicians promising benefits that others would pay for.
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Madsen Pirie 
The ethos of “Keep it simple” needs extending to the law as well. Common Law seemed to work reasonably well for centuries, especially when it was relatively easy and cheap to embark upon a court case to settle an unclear section of law.
Nowadays we seem to need to use ruinously expensive lawyers for even the simplest of tasks, which to my mind is a strong symptom of a partly broken system. Worst than this, there is little attempt to make laws and rules machine-searchable which, whilst it would not solve the byzantine complexity would at least off-load the complaince burden onto machines.
Hideously complex tax systems benefit nobody. Eventually people simply work around them, for instance by using cash in hand, barter, Bitcoin or intrinsic value coinage such as gold and silver. Taxation is supposed to be simple, easily paid and low.
Finally, the Tax Office has a blanket exemption to legal sanction for making mistakes. This needs to end; for it to work everyone and everything must be equally subject to the Law.