How is ATFM handled in the USA?
The problem with working together on a global scale or even trans-Atlantic is the long time and distance between. Flow control at least in the U.S. (and I'm sure elsewhere) is more short-term (1-2 hours out), mainly based around airport acceptance rates (AAR) which can change hourly or even more frequently for example because of runway configuration changes, or weather or visibility changes. There is also short-term projected sector saturation issues, and short-term sudden localized things like weather buildups that can come and go.  

That means for trans-oceanic flights you can't effectively implement departure metering (the main tool in the U.S. for flow control) or ground stops because you can't predict 5-10 hours in advance the traffic level and acceptance rate at the destination airport. It's much more effective to wait until they're back in radar coverage and closer time-wise to the destination when flow control calculations will be more accurate, and controllers can achieve miles-in-trail spacing requirements with quick radar vectoring. Over the ocean, outside of radar coverage, significantly adjusting in-trail spacing is more difficult because you really only have speed adjustments which are limited because of the narrow aircraft envelopes at high altitudes.   

For situations where there will need to be long-term flow control (such as, the only other runway is suddenly closed and will be indefinitely), we already do have a manual process to implement flow restrictions trans-oceanic, by each facility passing restrictions to adjacent facilities, on and on up the chain.  For example, Shanwick can tell Gander we need 10 minutes all aircraft all tracks landing EGLL, Gander tells Boston 12 minutes in trail, Boston coordinates with U.S. command center, etc to ensure Boston doesn't get overwhelmed with EGLL-bound aircraft. Those kinds of things happen very rarely though, so it's probably not worth connecting our different automation/flow control systems together and instead just keep handling it manually on a case by case basis.

(Source: I'm a former FAA controller and worked in flow control/Traffic Management Unit for several years).