OK, before I give you any definitive information lets explore all the options. I know you'r simply contemplating putting in insulation between the joists, but as that requires lifting all the floorboards with all the damage that could incur plus the cost of insulation/acoustic bats etc. both cost and time are going to be a heavy investment, any mistakes now could therefore be costly.
I'm assuming this is a bought property i.e. not landlord responsibility? Also you say the floor/ceiling construction between flats is, from bottom upwards, plasterboard - 3" joists @ 1' foot spacing and floorboards, no mention of an ash layer, which in older buildings was both the sound deadening and the fireproofing, so what's happened to that?? but that's another question.
If I've got it right so far and interpret your situation correctly you suffer from occupancy noises as apposed to noisy neighbours and you want to start in the kitchen you really should identify any peripheral avenues the noise may be coming through (under floor acoustic insulation may simply divert to lateral noise) Look for service shafts, pipe penetrations (in cupboards) etc.
Now let's get down to that insulation. By far the cheapest option would be acoustic underlay, properly installed some claim to better the current regs, you would have to research this yourself, to suit your particular floor covering. Acoustic insulation should be available locally or can ordered online. Where the boards run under drywall partitions have a look at their direction of run (lengthwise) the joists should run in the opposite direction meaning you need only cut each side of the partition and feed the insulation under and through.
I would seriously try out acoustic underlay first, it may seem expensive at first for what it is but if it works you could save yourself a lot of money in the long run...pinenot
