Without the possibility for advancement and/or monetary gain, what would drive people in such an organization to move forward?
This is not true of all flat organizations, but in the organization that is coming together at present, there are no monetary impetum, at all. If one person benefits, so does everyone in the group. The primary impetus for advancement is to help your neo-tribal relations.
Also, without money as a means for exchange/business, wouldn't something else just take it's place, therefore making that new thing/things the defacto "money"?
The only business will be the "market of the others" to borrow the term used by the Zapatistas. Internally, resources are shared, products are shared, and land is shared. The only thing that is not shared is housing and personal possessions. The market of the others is a requirement only because capitalism dominates the country and we have to pay property taxes and buy things we can't produce. However this arrangement is temporary. Once our organizations are able to provide for every need internally, we will not need money.
For example, you manufacture knives. For you, those knives are money. If you make better knives than another cutler, your knives would demand more goods in exchange than the other guy's knives. So, how is that "cashless", how is that not capitalism, and how would such a society not create new barons of industry?
In our communities, I will give my labor to others, just as they will give their labor to me. I will be as rich as everyone else. And I don't mind it at all. If I created only for money, there would be no reason to create new things, only what sells out. Just one style, with no new challenges.
Could you maybe post a summary?
We Leftists are notoriously long winded. Rather than me re-inventing the encyclopedia, I will recommend several books and videos.
Books:
Mutual Aid: A Factor of Evolution by Peter Kropotkin
The Communist Manifesto (only 40 pages, took me just 2 hours to read it) by Marx and Engels
Democratic Confederalism by Abdullah Occlan
Videos:
Anarcho-Syndicalist Organization
https://youtu.be/0RwlaNva_4g(In my opinion, and this opinion is shared by many people, Pure by-the-book Anarcho-Communism can only be attained through Anarcho-Syndicalist organization, because there are no rulers, no hierarchy, and there is always the option to opt out. This is vastly different fro the State-Communist representative republic model which does not work.)