  We seek the possibility of a disorder driven transition in a tight-binding
lattice with a flat band using complexity parameter approach. Our results
indicate the existence of a localized to extended states transition with
increasing disorder, insensitive to disorder strength, in weak disorder limit;
the spectral statistics at the critical point corresponds to a critical
Brownian ensemble, a non-equilibrium universality class of random matrix
ensembles, intermediate to Poisson and Gaussian orthogonal ensemble. With
increasing disorder, the statistics again approaches Poisson limit indicating a
localization -> extended -> localization transition of the wave-dynamics. Our
analysis also reveals a hidden connection of weakly disordered flat bands to a
wide-range of other complex systems including standard Anderson Hamiltonian.
