$$\int_0^t dt_1 \int_0^t dt_2 \int_0^t dt_3\, B(t-t_3)F(t_3-t_2)
S(t-t_2)F(t_2-t_1)F(t_1) \\
=\int_0^t {dt_2}\, (B*F)(t-t_2)S(t-t_2)(F*F)(t_2) \\ 
=\Big(\big((B*F)S\big)*(F*F)\Big)(t).$$