With the cap-based approach working during charging and discharging, there is no reason that you need to move a lot of current through. I would think even 200mA might be enough. The only reason you need an amp, or more is if you are trying to correct a fairly large imbalance, in a relatively short period.
There are two techniques to doing battery management. One is that you don't worry about balancing at all, and in essence, individually charge each cell to whatever its max level is, and then monitor each cell to make sure it doesn't discharge too far. To charge, you either use individual chargers on each cell, or you use a shunt-based regulator on each cell that will bypass whatever current the cell can't absorb during the final CV part of the charge cycle so that the next cell in series can have all the current available, if it is trying to "catch up" with the rest of the cells.
The second type of battery management is to try and end up with all the cells to be at the same voltage level/SOC at the end of the charge process. In many of these designs, shunts are also used, but in a different fashion. Instead of waiting until the cell is at the cutoff voltage, the shunts will bleed off current all the time for the cells that have higher voltage, which has the effect of slowing down the charging of those cells, in order to let the lower voltage cells catch up. The trick here is that you have to pick a current that is high enough to overcome whatever the worst case imbalance is likely to be, over the charge cycle. Most of the BMS units that come with the cheap "duct tape" packs only use about 100mA of bleedoff current and what the charger does is just keep supplying a "trickle" charge until the cells finally balance. Their own instructions say that this process can take up to 10 hours for packs with significant imbalances.
One thing that really needs to be factored in is just what kind of imbalances are considered "normal". I haven't used any of the lower C-rated Chinese LiFePO4 cells, but I have quite a bit of experience with a123 cells and now with LiFeBATTs. Packs made with healthy a123 cells, will rarely have imbalances more than 1-2%, under normal use. I have a couple of packs like this and they stay so close that for the most part, I just bulk charge them using a Zivan NG1. Ocassionally, I will use my VoltPhreaks individual cell chargers on these packs, but this doesn't really get them any more balanced. I also have a couple of packs that have cells that have been "stressed", mixed in with healthy cells. The stressed cells were in two packs that got over-discharged. Some cells went all the way to zero volts, and are truly dead. Some got down under 2V, between 1.6V and 1.8V and these recovered, but now are the stressed ones, with slightly reduced capacities (about 10%, near as I can tell...). The rest of the cells never got below about 2.5V and they are now still as strong as ever. Anyway, these packs with the stressed cells typcially have imbalances as high as 4-5%, but with these I don't think the answer is to simply drag down the level of the healthy cells so that they always equal the lower level of the weak cells. Instead, I always just individually charge each cell in these packs, just to make sure each one gets a full charge, whatever that happens to be.
What I'm seeing with the LiFeBATT cells is that I have yet to see an imbalance more than about 2%. This tracks with what the factory in Taiwan keeps telling us, which is that by using very tight quality control during the manufacturing process, and by extensive burn-in testing and cell matching, they claim cells will stay within 2%, period. They do capacity and IR-based cell matching when they build their packs, and they do the same with loose cells, which come eight to a box. I've got one 16-cell pack that has cells from two boxes, and all the cells from one box stay within about 1% of each other, as do the ones from the 2nd box, but the difference between the two batches means that the total imbalance is just under about 2%, worst case. Now I haven't used this pack more than a few cycles yet, but I will keep a close eye on it to see how balance might change over time. With my other LiFeBATT packs, I didn't pay much attention to which cell came from which batch, but overall, the cells in all the packs never have had an imbalance greater than about 2%.
Anyway, getting back to how much current is really needed for a cap-based approach, I think at least three factors need to be considered. First, how much imbalance should this be designed to overcome? I'd say 3% is probably a good starting point. Next in how short a time does this imbalance need to be corrected? Finally, closely related to the second factor is what is the max charge current that is being used? If you are trying to charge a pack at a 1C rate, or better, you will need to switch more current between cells to keep up than you will if you are only charging at a 1/2C rate. Also, if you are only trying to correct imbalances during the actual charge process, you will need more switched current than you would if the balancing is allowed to happen all the time, or at least during discharging and charging. I haven't done the math, but my rather generous gut tells me that 200-300mA might be plenty if the balancing is allowed to happen during discharging and charging, and maybe even as low as 100mA, if allowed to work all the time.
--Gary