Some people choose not to carbonate their Kombucha. This is also a question of personal taste. The SCOBY will seal (though not completely) your batch in the jar. When you harvest the batch it will be slightly carbonated, though not like store bought. Uncarbonated Kombucha tastes something like apple juice (depending on how long you choose to ferment).
There are two kinds of carbonation: natural and forced. Natural carbonation happens when the liquid is allowed to ferment a second time (called conditioning or secondary fermentation) in an airtight container. Beer, champagne and hard sparkling cider (when made in small batches the natural way) can all be carbonated using secondary fermentation.
Forced carbonation can be done at home but it is not cost effective and requires a lot of equipment. This is usually done by large manufacturers using CO2 tanks and other equipment.
For the kombucha to properly carbonate (this can be a question of taste, I like a very carbonated Kombucha similar in level to soda or seltzer water) it is important to give the yeast extra sugar in some form. Fruit juice works wonderfully for this. I’ve also found adding pieces of fresh ginger really help carbonate the kombucha quickly. (The yeast love ginger!). It must be fresh however. I usually peel and dice the ginger and keep it in the freezer.
I’ve also found that as your SCOBY(s) matures carbonation will happen much more quickly. When I first started making kombucha it would take the bottles 7 days or so to carbonate. Now after many batches they carbonate in 2-3 days depending on what I add. Plain Kombucha still takes a long time to carbonate and will usually never carbonate to the level of Kombucha that has fruit juice and ginger added to it.
The type of container you use will also affect carbonation. Read here for more.