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We theoretically and numerically investigate the evolution of discrete soliton in a 1D linearly chirped nonlinear waveguide array (WA). The discrete soliton is self-accelerated inside the transversely chirped WA and emits a \textit{dynamic diffractive resonant radiation} (DifRR). The radiation appears when soliton wave-number matched with linear radiation wave. Unlike uniform WA, the DifRR can be excited even for zero wave-number of input soliton when the waveguide channels are chirped. The transverse modulation due to chirp conceptually imposes a linear potential which acts as a perturbation to soliton dynamics and leads to a monotonous wave-number shift of the propagating wave. Exploiting perturbative variational analysis we determine the equation of motion of soliton wave-number and use it to establish a modified phase-matching condition which takes into account the soliton wave-number shift and efficiently predicts the dynamic DifRR. A startling effect like generation of dual DifRR occurs as a result of the interplay between self-accelerated soliton and its initial wave-number. We exploit the modified phase matching relation to understand this unique phenomenon of dual radiation and find a satisfactory agreement with numerical result in radiation wave-number calculation.