A hydrometer measures fluid density (AKA specific gravity). Water has a specific gravity (s.g.) around 1.000.
Water with sugar in it has a higher s.g. because the sugar is more dense than water. The s.g. of kombucha depends on how much sugar you add, but probably somewhere in the neighborhood of 1.010 to 1.030. Juice probably ranges higher, around 1.030 to 1.060.
Yeast converts the sugar into carbon dioxide gas and ethanol. This changes the density because the ethanol is less dense than sugar. By measuring the change in density we can determine an approximate level of alcohol.
The alcohol level in kombucha is tricky to measure because besides yeast there are also bacteria complicating matters by converting some of the sugar into lactic acid and much of the ethanol into acetic acid. Therefore relying on s.g. measurements alone will provide a poor estimate of the alcohol level.
If you know the starting and finishing specific gravities we can help determine a ballpark
maximum possible ethanol level. The ethanol level declines the longer it sits at room temperature with oxygen exposure.
Although you
can measure the alcohol level, you need more advanced instruments and techniques. The first step is learning how to read a hydrometer

Normally you put some of the kombucha in a clear tube large enough to hold the hydrometer, and put the hydrometer in so it is free floating. Look at it from the side, and determine the number on the s.g. scale by using the bottom of the meniscus. Read it to the nearest 0.001.
Fluid density changes based on temperature, so you want to have the fluid at the same temperature as the calibration on your particular hydrometer; usually it's 68°F or 60°F.
It's complicated but I hope this makes sense. Welcome to HBT!