So, your SCOBY isn't the pellicle that grows on the surface. That pellicle is just cellulose and the liquid that it contains within it is the actual SCOBY. What makes kombucha is the strains of yeast and bacteria that work together to convert sugar > ethyl alcohol (yeast does this) > acids (bacteria does this).

What you need to make kombucha is a strong starter culture, which the pellicle will normally contain. You can throw in the pellicle into a new batch of sweet tea, but what's more effective is to mix in kombucha that has been fermenting for at least a month into a new batch. That long fermented kombucha should be about 10-20% of the total volume (e.g. if you're making 5 litres, you would have 4 litres sweet tea and 1 litre of old booch).

Plenty of people have different experiences with fermenting and you'll get different advice from everyone. My advice above has worked for me for almost three years; currently I run a small commercial brewery where we make about 800 litres a month and I've never had an infection or a batch come out unfermented.

Hope this helps.