Hi! I'm having problem while I play relatively fast tempos like 16th notes at 115bpm. As my thumb's nail moves over the strings (I'm using floating thumb technique) it creates a scratchy sound which is a bit annoying. It only appears when I cross the strings and use three finger plucking. I've tried to change my angle of my thumb but it slowed me down :/

How can I get rid of it? Or should I get rid of it at all?
if i understand you correctly, that's normal. you might want to try flatwound strings to cut down on the noise.
Quote by Skeet UK
I just looked in my Oxford English Dictionary and under "Acoustic Guitar", there was your Avatar and an email address!
I would say that you need to trim your nails and work on the angle. If your thumb nail is causing unwanted string noise, that a sign you need to work on your technique. It may slow you down now, but you'll regain speed once you get more comfortable with it.

I'd like to see a pic or a demonstration of what angle your thumb is when playing. A video would be better, too.
...it was bright as the sun, but with ten times the heat
Well; if you do not use your thumb for playing, you could just wrap a band-aid around it so that the thumbnail does not contact the strings.
"Maybe this world is another planet's hell?" - Aldous Huxley