I would think it would work fine, however the flavoring will dissipate and be hardly noticeable rather quickly. I would not use a flavored kombucha personally. I have been making my own for well over 9 months now. This is how I started...

Made a batch of black tea; cannot remember which kind as I buy all sorts from a bulk tea shop in town.

Added a cup of raw organic sugar; I use rapadura Sugar now. The rapadura makes the tea very cloudy, but I believe it is richer in minerals as the BSM has not been refined out.

Poured in a 16oz bottle of RAW Kombucha tea... cannot remember the brand now.

Took about 10 - 14 days for the first batch. Depending on weather and temperature, the batches I brew now are ready in 5 to 7 days. I usually drink the whole gallon in 5 days or so.

I rotate 3 gallon jars always having one for drinking, one brewing and one resting with a culture for the next batch. I have never refrigerated it, but may do so in the future. I drink it all before it gets too vinegary.

I now use Sencha or Bancha green tea and rapadura sugar. I do brew a black tea on occasion, but find the green more to my liking.

grz

You could probably just strain out the floating stuff, brew a quart of black tea with 1/3 cup Sugar and when it's cooled, put what you've strained out into it.