I am looking for a correct form of the word: thrashing(?). You say "let's get thrashing" when you move your hands violently while do finger painting. It the word correct?
Two minor issues with the choice of word thrash:
To thrash means to whip about uncontrollably and with significant or great force. It usually implies both A) the thrasher isn't being careful or cautious and B) the thrasher might damage something. Someone might think you are implying that the canvas could be damaged or you literally don't care if paint gets everywhere except the canvas.
When a person thrashes, if no instrument (e.g. specifying you are thrashing with something) or target/object is specified or implied, the default is the entire body. So when you say "Let's get thrashing" it sounds weird. As fingers/painting is not typically a violent activity, it can fail to provide enough context for someone to assume you mean just their fingers without thinking about it for a second.
There isn't a good word that's less stronger than thrash that really works for finger painting. Whip, wipe, smear, etc. all won't sound right.
Finger-painting is a messy activity though, since you actually touch the paint, so something like "Let's get messy and start painting" may be better to say.