Hi all, first-time poster long-time forum viewer. I am a beginner acoustic guitar player, self-taught, hoping to be a skilled finger-picking player.

One of the most annoying problems I am encountering is when I place a finger on the fret board, play the note and when I lift the finger to place it on another fret, there seems to be the open sound of that string being played.
Flicking? Don't think so, I am trying to gently raise it, it feels like it slightly get's stuck on the fingertip as I raise it even when I do it gently.
This will happen to everybody. You will not be able to suppress all noise, it isn't in the nature of the instrument...however since you are playing with your fingers, use them to mute the open string sound when possible. Make sure you are simply lifting your finger and not moving those strings to the sides when you are done playing the fretted notes.

Although not on an acoustic guitar, when I play high gain electric guitar stuff, I will sometimes bend strings out of the way with my picking hand to ensure there is no bumping into open strings when using vibrato. Some guitar players wrap a hairband around the nut of the guitar for further reduction in noise.