Fraction of labour force providing income redistribution services What % of the labour force for an OECD country like the UK (mostly civil service I'm guessing) deals primarily with income redistribution, rather than income generation? Would a simple flat income tax at 40% and a universal basic income have the extra benefit of letting more people enter the value adding economy?
"What % of the labour force for an OECD country like the UK (mostly civil service I'm guessing) deals primarily with income redistribution, rather than income generation?" 


It seems like you are talking about the   Volunteer sector .

in the UK particularly  NVCO reports in its 2012 almanac: 


  What is the relative size of the voluntary sector workforce? 
  
  The voluntary sector is a major employer. An estimated 765,000 people work in voluntary sector organisations. This is 2.7% of UK workforce, and compares with 25% who work for public sector employers, and 72% who work for private sector employers. The voluntary sector paid workforce is roughly the same size as the number employed in restaurant and catering in the UK (around 770,000).


For your second question:


  "Would a simple flat income tax at 40% and a universal basic income have the extra benefit of letting more people enter the value adding economy?"


I see no connection between an income tax and creation of jobs. Labour supply models would indicate that we  will see changes in the amount of labour supplied by a given worker in the presence of income taxes and will end up with some deadweight loss.

This is not fully explained but a clearer understanding of the effect of income taxes  on welfare will come from reading up on labour economics models.

Hope this helps.