An easy enough solution might be to take a cut when money is moved in to or out of Flattr, but to take nothing when moved between Flattr accounts.
If the money then circulates then that's OK. If the money is withdrawn then take a good cut of that.
One downside to that is that the more popular it becomes, the more 'currency' the flattr-coin becomes, it simply circulates with people neither depositing it nor withdrawing it. However, flattr are then effectively become a central bank and that isn't a problem.
The real problem with not taking a cut of moving between flattr accounts is that people would sell flattr through side channels to avoid flattr taking a cut. So you'd pay me cash and I'd transfer to you the flattr coin on platform.
And if it took off in a big way then money laundering becomes a problem and the cut would not cover the cost of KYC etc.