To give a notion, it is something like "to do an action heavily, with a special effort, intension, pressure, enthusiasm".
If you want to convey the impression of approval of the energy/enthusiasm (either genuine or ironic), the ideal word is gusto: see the definition in the Cambridge Dictionary. You can make it into an adverbal expression (and that's how it is most often used) by saying with gusto.
He is playing the piano with gusto
He is painting with gusto
This expression can be applied to virtually any activity.
From Merriam-Webster:
flail
transitive verb
1 a : to strike with or as if with a flail · The bird's wings flailed the water.
b : to move, swing, or beat as if wielding a flail · flailing a club to drive away the insects
2 : to thresh (grain) with a flail
intransitive verb
: to move, swing, or beat like a flail · arms flailing in the water
So you could flail a piano keyboard with your fingers, or flail a canvas with a paintbrush (definition 1a). Alternatively, you could flail your fingers or arms while playing the piano, or flail a paintbrush or your arms while painting (definition 1b). Moreover, according to the definition of the intransitive verb, your fingers or arms can flail during either of those activities.
This verb cannot describe all actions that one could perform "heavily," however; for example, if you were crushing eggs by stepping on them with a heavy boot, flail would seem incongruous; the reader might be confused about whether you were actually wearing the boot or swinging it with your arm. And if you were pulling weeds up from the ground in your garden energetically, flail again would be wrong since you are applying force to pull something from the ground rather than to strike something.
As pointed out in a comment, one should be careful about the use of flail in the context of something artistic. Usually when someone says that a person is flailing their hands on a piano, the implication is that they are not playing well. If you want to convey the sense of playing enthusiastically and well, you might want a different word.
Possibly, here are some verbs
There's no single verb to cover both meanings. There are several adverbs you could use to describe the playing or painting. Such as: playing loudly/noisily/violently, or painting wildly/expressively/violently, etc, etc.
"Exert" seems to have the meaning you described.
E.g:
"He exerted himself at/on the piano/the canvas."
"Inflict on/upon" involves violence or agression (sounds sarcastic as in over-enthusiasm, excessive loudness etc)
"He inflicted himself upon the keys / canvas"
Also,
"Applied himself to the piano/canvas with abandon / earnest / all his might / gusto etc" "Tackled the keys/canvas ..." "Wrestled with the piano/canvas"
English is a strange language, no?
Depending on context, writing style, ethics and taste you could use many words which describe the passion and vigour in which artists work.
In the same manner you can also elucidate upon the grace and elegance with which the pianist is performing the piece, but for your needs these are not valid.
It is all about context - just like life, language needs a context in which to be properly understood.
The creative process is just that, an intensely absorbing moment in which the creative is expressing their inner most feeling.
A lot of emotions go into driving our creative moments.
For example, if you would like to show an obsessive process you could say the artist was possessed.
Again, context is imperative.
A single word for you needs would be 'pathos'.
It comes from the Greek and indicates an action done with passion and extreme focus - a purely zen moment.
Hope this helps.
