Any time I try to draw or paint in Sketch, the brushes do not taper or have pressure sensitivity. It doesn't matter if I use my finger or a stylus, every line looks the same. How can I enable this feature? Or is it only available on the iPad version of the app?
You're only going to get "pressure-sensitivity" with a bluetooth stylus and iPhones don't have bluetooth stylus support.
But, I think you should be able to make some of the stroke adjustments you're wanting in the Brush Settings panel. To open that tap on any of the brushes in the main tool set. At the bottom of the Color menu that opens tap on the Brush Settings (three sliders) icon at the bottom of the Color menu. You'll be able to make some brush adjustments there.
I hope it's what you're looking for.