Designing Startup Network for Flyback Controller
1) Would this cause some imbalance in the caps?


Yes, but not significantly over the time period and current draw you are considering.


  2) How do I calculate a proper value for C16?


This can be calculated using equation 9 in section 8.2.21 of the datasheet. It is dependent on IC operating current (including Gate drive output) as well as capacitor charging current and time taken for the auxiliary voltage to take over (which is determined by converter output current and capacitance).      


  And the time this circuit will actually take to start the controller?


Probably Longer than you want. The formula for capacitance when (dis)charging at constant current is \$C = i * t / V\$. 
Assuming the minimum charging current of 140 uA, 2.3 mA operating current + 1 mA Gate drive current, 9.35 V between VDD turn on and off, and 10 ms before the auxiliary voltage takes over, the capacitance required is (2.3 mA + 1.0 mA - 0.14 mA)* 10 ms / 9.35 V = ~3.4 &mu;F. But if you use this value it could take ~1.8 seconds to charge the capacitor to the maximum startup voltage of 23 V (actually even longer, because the divider capacitors will 'unbalance' significantly over this time period). 

To get the charging time down to 10 ms C16 must be no more than 140 uA * 10 ms / 23 V = ~61 nF, but this may only hold the voltage up for 61 nF * 9.35 V / 3.16 mA = ~180 us. So the controller will have to start up and charge its output capacitor in less than 180 us once the VDD turn on voltage is reached. This time adds to the total start up time, so to get a total startup time of no more than 10 ms the charging time must be even less. 

To achieve your desired startup time you will probably need a much higher charging current.