The beauty of clawhammer is in it's economy of motion. As the index (or middle) finger moves in to to strike a string, the thumb comes to rest against another string. As the hand moves away from the banjo, the thumbs slides off the string it was resting against sounding that string. Two notes created by two motions of the right hand; one as the hand moves into the strings and the other as the hand moves away from the strings.
If you are "flicking" with the index finger, you probably aren't "catching" the thumb on a string at the same time as the index strikes it's string. This means the thumb and index are moving in and out of the strings as separate motions. Four motions instead of two; in and out with the index and then in and out with the thumb.
This means that until you get the thumb to come into it's string at the same time that the index strikes it's string, you will probably be limiting yourself to half your potential speed! You will also be introducing tension into your right hand which is never a good idea.
Thanks... Mike