Heya~ looks like i can give a few tips here:

O yea...my record for longest quickening chain? 22

anyways here it is:

When you first start a quickening, start it with a lvl 1 or lvl 2 quickening first. The lvl depends on how much mp you will use (3 gold circles if you have all 3) If you have all 3 quickening, go for lvl 1 or 2. If you have 2 quickening, go with lvl 1 quickening first. This is so that after the first quickening is activated, the same character has mp left for another one, or a mist charge.

Second: If you see a quickening available, but also a mist charge for another character, go for the mist charge first. However, if time is short, go for the available one. The mist charge is random, it can charge up the character it was given to, or it can mist charge others. If you have enough time, see only 1 quickening available with a mist charge for another, go for the mist charge. Chances are, you will have 2 more characters available with renewed quickenings.

Reflex is key here. If you do not see any quickenings, shuffle quickly with the R2 button, but do it with just enough speed so that you don't accidentally shuffle and skip over an available quickening. This happened to me a few times and ruined my quickening chains. If, after you shuffle, you see a mist charge and 1 quickening, try out the 2nd tip above.

After you have done a mist charge, if you see another mist charge pop up, go for that as well, given time is enough. One major factor that can chain quickenings for long periods of time is the mist charges. Although the amount it can charge is random, its better than using up all available quickenings and having to shuffle because you have no mp left. This is how i chained 22-chain style~ Ending AOE was Luminence I think....or was it something else? (I think it was ice-like aoe...forgot what it was called)

Well...there you go, my few cents.