Budgies are lactose intolerant so I wouldn't recommend giving them Kefir, either
There are water kefir grains which do not rely on a milk substrate... I assume that's what the original post was referring to...
It has quite different advantages to Apple Cider Vinegar though, being high in the bacteria and yeast that it is fermented by.
Apple cider vinegar is made by the same bacteria and yeasts (possibly slight differences, it's nearly impossible to tell without a purified culture), just under more anaerobic conditions to shift the metabolic processes in favour of producing acetic acid. Kombucha contains acetic acid, as well. You can even grow a scoby from balsamic vinegar... It wont be a pretty scoby, and you'll probably have mould, but it works... No peer-reviewed assays have found significant levels of anything in kombucha that isn't found elsewhere in our diet (and have found it comparable to vinegars).
I've also read reviewed assays that have made me skeptical of the claimed sugar contents, although I haven't had enough money to buy my own testing reagents to confirm on my own batches...
Not trying to slam kombucha or kefir brewers, I personally love the stuff, and I researched it for awhile before I started brewing because there have been some medical cases that were technically linked to home-brewed kombucha (on the record, at least)...
I just argue that there isn't enough evidence to suggest its benefits over vinegar, and without extraordinary qualifications I do not think we can ethically experiment on our birds, no matter how good our intentions may be.
Basically, you're free to experiment with your own body, but when it comes to animals who can't give consent, I would stick to tried-and-true methods... I'm sure this isn't what the original post was asking for though... To which, my answer would be that there isn't enough information for us to tell you for certain.
A very interesting question, though, nonetheless.