Is there any accurate model that can take flight data, plane identifications and compute the amount of fuel that the aircraft would burn flying a set route over the Atlantic ocean.
I am sure every airline has such a model, which will include actual wind and temperature information, but it will contain proprietary data which is not publicly available, unless you have a proven interest and signed an NDA with the airframe and the engine companies. Boeing is actively marketing such software to it's customers. For first-order estimates, Federico's comment is a good start, but you will still need fuel flow and L/D values.
A range of similar software exists, but here the quality of the output depends mainly on the quality of the aircraft and engine models. While Boeing should know their aircraft well, the authors of independent software like Piano or APP have to guess the right values, but still sometimes such tools will be precise within one percent. Piano even offers a free version called Piano X, but you will need to burden yourself with a Windows installation to run it.
If you need even more precision, there are commercial packages which do this, first of all J2 Aircraft Dynamics. But this does much more; fuel flow is only a tiny aspect of the full package. Eurocontrol is supporting BADA, which is a tool for computing aircraft trajectories, but it can also compute the full flight and contains an extensive set of detailed aircraft datasets. Access to BADA is restricted, however, and you will need to acquire a license.
If you want to assemble your own tool, JBSim would be a good start. Write a wrapper which calls JBSim repeatedly and keeps track of the aircraft trajectory, and integrates the flight parameters along the way. But you will still need to get the aerodynamics and engine data from somewhere.