BQ77910A balancing current limit

The balance current with the external FET is likely limited by the heat you can dissipate in the resistor array you use for balancing and possibly by the FET...  The FET should have characterized performance at low Vgs, possibly 1.8 or 1.6V, these FETs may have a Rdson at this voltage which limits the balance current due to heating of the FET.

How much blanace current you need will depend on several system parameters such as the cell mismatch in self discharge, any asymmetrical load you may have on the cells, the time between charging and the amount of balance time at charging.

The bq77910A uses a simplistic balance algorithm intended to maintain a relative balance of the cells by balancing at a low current for a long time, but this depends on how the part is configured and how it is operated in the system.  It will provide the best features if a charge detection signal can be provided since balance can be set to balance while the charger is detected.

For example if your 4s system has 1 cell discharge 10 mAh more in a discharge cycle than the others through different loading or self-discharge mismatch, you would want or need to balance the other 3 cells down by 10 mAh during the next charge cycle.  If you have 100 mA of balancing current with a bq77910A, the part will balance ~ 100 mA x 1/8 hour per balance interval of the part, or 12.5 mAh per interval before considering the balance/measure duty cycle.  If balancing is set up to run the minimum 1 hour (8 interval) timeout and the device voltage calibration is perfect the cells would be approximately balanced after the 1st 3 intervals. After the next 4 intervals the pack is again balanced, after the final interval one cell is slightly low. After the next discharge cycle there are 2 cells with the mismatch.  After 8 intervals there will again be 2 cells mismatched.  The pack will continue through this sequence maintaining a relative balance.  A lower balance current may provide less adjustment of the cells as long as it can keep up with the self-discharge.

You may find that for 4 cells it is more convenient to use a gauge with an AFE rather than the '910A protector with the bq34z100 gauge.  There are a number of device options for 4 cell packs.  Of course as mentioned in the post you referenced, there are other considerations such as the cell and interface type for the final selection.