The Institute for the Study of Labor has published Is a Flat Tax Feasible in a Grown-up Welfare State? by Clemens Fuest, Andreas Peichl & Thilo Schaefer.  Here is the abstract:

The success of the flat rate tax in Eastern Europe suggests that this concept could also be a model for the welfare states of Western Europe. The present paper uses a simulation model to analyse the effects of revenue neutral flat rate tax reforms on equity and efficiency for the case of Germany. We find that a flat rate tax with a low tax rate and a low basic allowance yields positive static welfare effects amounting to approximately 1.8 per cent of income tax revenue but increases income inequality. The increase in income inequality can be avoided by combining a higher tax rate with a higher basic allowance. But in this case the efficiency gains vanish. We conclude that, due to their limited efficiency effects and their problematic distributional impact, flat tax reforms are unlikely to spill over to the welfare states of Western Europe.