Modern "High Frequency" ballasts are electronic ballasts, similar to those within the Kino fixture itself. Older style ballasts, known as "instant start" or "quick start" ballasts are magnetic, meaning they pulse at the line frequency of the power they're wired to. In the U.S. they"flicker" 60 times/second, in the U.K. is 50/sec (50 hz). High-frequency ballasts also flicker, but 40,000-60,000 times / second, so it's very unlikely you'll be shooting fast enough to catch a ballast-related flicker on electronic ballasts.
If you remove the covers of the lights you're re-lamping, you can read the ballast to figure out what you have. Don't assume every fixture has the same ballast! Especially in large offices, as lights have problems and ballasts burn out, they get replaced (usually with the cheapest pieces possible). Also note that electronic ballasts are significantly more efficient than magnetic ballasts, and you will almost always see a large gain in output from the same tube if hooked to an electronic ballast.
As for flicker, if you're shooting at an off speed (see Davi'd link to the safe framerate tables), you'll probably see some. However, with older tubes you may ALSO see flicker, due to the ballast being unable to sustain the plasma within the tube. This can happen even with electronic ballasts, so be aware of the age of the tubes you're putting in. Fluorescents have mercury in them, which brightens the output of the lamp, and helps create the correct frequency of radiation to excite the coatings inside the tube. As the tube ages, the mercury migrates into the coatings and glass, away from the electrodes and causes unstable "burn" of the tube, which can appear as a color shift or flicker.
Freya also makes a good point - Kino is not the only game in town when it comes to color-correct tubes. Find a lighting wholesaler that deals in fluorescent, and ask what they have in the way of high (>89 or >91) CRI tubes of the fitting and color temp you're looking for. Chances are, they'll have about 5-6 different tubes that fit your needs, and prices significantly cheaper than Kino.