Irreducible complex flag manifolds are of the form $X=G/P=G_u/K$ where $G$ is a complex simple Lie group and $P$ is a parabolic subgroup, and $G_u$ is a compact real form of $G$ and $K=P\cap G_u$. As a rule, the connnected automorphism group $Aut(X)^0$ coincides with $G$, with the only exceptions:
- $X=G_2/U_2$, $Aut(X)^0=SO_7(\mathbb C)$.
- $X=Sp_r/Sp_{r-1}U_1$, $Aut(X)^0=PSL_{2r}(\mathbb C)$.
- $X=SO_{2r+1}/U_r$, $Aut(X)^0=PSO_{2r+2}(\mathbb C)$.
You can find a discussion in chapters 3 and 4 in Lie group actions in complex analysis, by Dmitri N. Akheizer, Aspects of Mathematics, vol. E27, Friedr. Vieweg, Braunschweig and Wiesbaden, 1995.