We investigate the effect of strain-induced gauge fields on statistical distribution of energy levels of triangular graphene nanoflakes with zigzag edges. In the absence of strain fields but in the presence of weak potential disorder such systems were found in Ref.  to display the spectral statistics of the Gaussian unitary ensemble (GUE) due to the effective time-reversal (symplectic) symmetry breaking. Here show that, in the absence of disorder, strain fields may solely lead to spectral fluctuations of GUE providing a nanoflake is deformed such that all its geometric symmetries are broken. In a particular case when a single mirror symmetry is preserved the spectral statistics follow the Gaussian orthogonal ensemble (GOE) rather then GUE. The corresponding transitions to quantum chaos are rationalized by means of additive random-matrix models and the analogy between strain-induced gauge fields and real magnetic fields is discussed.