data1 = RandomVariate[NormalDistribution[5, 1.2], 1000];
skd1 = KernelMixtureDistribution[data1];
custom[a_] := ProbabilityDistribution[PDF[skd1, x+a], {x, 0, 10}, Assumptions -> a >= 0 && a < 2.5];

data3 = RandomVariate[NormalDistribution[6, 1.2], 1000];
FindDistributionParameters[data3, custom[a], ParameterEstimator -> {"MaximumLikelihood", Method -> {"FindMaximum"}}]

custom[a_] := ProbabilityDistribution[a PDF[skd1, x], {x, 0, 10}, Assumptions -> a >= 0 && a < 2.5];