Li-Ion or Li-Po cells never seem to discharge or charge at exactly the same rate.
When in series this is easier to deal with as you can measure the voltage across each cell and balance it during charging.
In parallel that is obviously not possible without separating them, so if one cells voltage is much lower than the others, it will draw more current. Eventually if they are healthy, they will all end up equal.
In practice the protection circuit on whatever they are powering should prevent the voltage falling too low to prevent damaging the cell, so they should not be too different.
I would not charge at 6A though, without knowing that one cell was not very low, and if it is possible it might be worth being able to charge each cell separately every 10 charges or so.
Last year started to use Li-Ion on projects, cell phone batteries are a very useful voltage, shape and capacity, and most of them have under/over voltage and over current protection built into the package, and some slightly bigger than AA also have built in protection.