Perhaps the implication is that he is holding his breath for, say, 5/6 of the time, then phasing inside and taking a breath for the other 1/6. His idle animation does include him zooming away every so often.
A speedster can definitely phase through a Kryptonian. He just merely passes through
Now if he really wants to hurt Superman, say pull out his organs, he just hurts himself.
There is no way he can expect to materialize is hand in Superman's body. He would be trying to displace something that is much more durable than him.
So, bottomline is that The Flash ...