What is the difference between a transferable flag and a non transferable flag?

I never heard of such a thing because a flag stops all personal actions-Promotions, schools, transfers etc.. Now since you are a PVT, if you are still in OSUT/AIT most UCMJ type actions do not follow you into your 1st unit.

A transferable FLAG goes with you when you're reassigned, such as an APFT failure.
A non-transferable FLAG does not, but also generally precludes you from being reassigned, such as the punishment phase FLAG that you mention.
Basically, the Army expects the action to be fully completed by the current unit of assignment before you go somewhere else to potentially become their problem. That keeps issues from being kicked down the road.
In your case, you will likely remain a casual until this issue is completed.

Not until you are finished the punishment phase.

AR 600-8-2. Don't go off of what people say though, the regulation may have certain situations that it can differ take a look for your self. Research ability goes a long way.