In this arcicle, a linear observer-linear controller approach is proposed for the robust trajectory tracking task in a large class of nonlinear differentially flat systems, including multi-variable nonlinear flat systems. A non-phenomenological model of the input-to-flat-output dynamics is proposed which only retains the orders of the Kronecker integration subsystems and, the control input gain matrix, as key controller design elements. The additive influence of the rest of the nonlinear state dependent dynamics, including exogenous unknown perturbation inputs, is considered as unknown but uniformly absolutely bounded disturbance that is shown to be algebraically observable and it can, hence, be approximately determined, to any desired degree of accuracy, by means of a set of linear observers with suitable, self-updating, time-polynomial internal models of the unknown disturbances. The controller design task is reduced to that of canceling the additive disturbances while imposing a desired linear dynamics, via estimated state feedback, obtained from the proposed observer itself. A convincing simulation example dealing with rather complex nonlinear physical system is provided. Two experimental implementations on laboratory prototype systems are also reported.