By making a rudder input you are creating sideslip.
The aircraft has two important static stability derivatives which are a function of sideslip. These are lateral stability and directional stability. Expressed mathematically both are the first partial derivative of moment (rolling and yawing respectively) with respect to sideslip.
So, when you make a rudder input the first thing that happens is the aircraft sideslips. Then the stability characteristics cause it to both yaw and roll. The only way a truly flat turn could be achieved would be in an aircraft with no lateral stability (either positive or negative), but retaining directional stability. I can't offhand think of any aircraft that has these characteristics - something like a Pitts must come reasonably close I'd guess.
The book I learned much of this stuff from was Donald McClean's "automatic flight control systems", which if you can find a copy may help a lot in working through the maths - it also has sample sets of stability derivatives for known aeroplanes that might help. ISBN 0-13-054008-0.
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