First remark, I really wonder, why it's so difficult to place a question in the correct forum?
Secondly, constant current would be the obvious method to charge a supercap effectively. Charging it through a resistor implies to lose half of the input energy, only a (ideally lossless) switching converter can charge it from a voltage source without huge losses. If current controlled, it would source 10 A. Alternatively, a constant current/constant power characteristic may be appropriate.
Thirdly, constant current is in fact the standard operation mode of the bq24640. Because it's just a controller without power transistors, most properties depend on the detailed circuit designs. You would want to refer to the TI datasheet and reference design to answer your respective questions. 10A charging current sounds feasible, however.