Answer: The whole business of rhythm syllables is pretty arbitrary. The main thing is to have some kind of system that relates to the division of the beat. In the case of sixteenths in compound meter, and I assume you're thinking of something like 6/8, 9/8, or 12/8 in which the beat is a dotted quarter, you're going to have 6 sixteenth notes for each beat, and they're going to be heard in three groups of 2 each. Personally I might just try one-ah, two-ah, three-ah for each beat's worth, changing the "one" appropriately. For instance, in 6/8 a measure would be "one-ah, two-ah, three-ah, two-ah, two-ah, three-ah." Eventually you'll get used to this to such an extent that you won't need the syllables, of course; you'll just hear the rhythm in your head.

As is often the case in music, scholars have developed elaborate systems for this. The Kodály people have one that I think I'll skip explaining here, in which quarter notes are "ta" and eighths are "ti ti", etc. The Takadimi system is another; it would put a "ta" on every beat, and I like the logic of that - then beats divided in two are "ta-di" and beats divided in four are "ta-ka-di-mi". In compound meters where the beat is in three parts one would say "ta-ki-da," which is easy enough. But for the specific case you're asking about it's "ta-va-ki-di-da-ma!"

Now I like the sound of that ta-va-ki-di-da-ma and if it works for you I say, use it. But it might be hard to remember. In fact, to me it's hard even to say; it amounts to a tongue-twister and I think if I had to concentrate on getting that right I wouldn't be able to handle the pitches, or even to chew gum at the same time. So I'm sticking with "one-ah, two-ah, three-ah."