i dont have much experience with importing custom models and textures, but i believe sometimes you need to make a texture called an ambient occlusion map and i believe that helps with how lighting looks on meshes. (that might not apply to thius case though)
I found solution how to do it in 3ds max.
Make regular texture for mesh (paint it over in Photoshop or some other app).
Go in 3ds max → Preference Settings/Gamma and LUT and turn on Enable Gamma/LUT Correction and set gamma to 1. After that textures will look darker in viewport. Assign vertex colors from texture (diffuse) to mesh. It will than look correct in Unreal.