Let $G$ be a real semisimple Lie group with finite center.
Definition 1 A real flag manifold is a homogeneous space $G/Q$ where $Q$ is a parabolic subgroup of $G$.
Definition 2 Let $K$ be a maximal compact subgroup of $G$ and $\mathfrak g=\mathfrak k+\mathfrak p$ the Cartan decomposition. A real flag manifold is an adjoint orbit of $K$ in $\mathfrak p$.
Question Do these definitions coincide?
Since $K$ acts transitively on $G/Q$, we have $K/K\cap Q=G/Q$. Therefore I guess the problem amounts to showing that $K\cap Q$ is the centralizer in $K$ of a certain element $h_0$ in the Cartan subspace $\mathfrak a \subset\mathfrak p$ which defines $Q$. I can easily see that $\mathfrak k\cap \mathfrak q$ is the centralizer of $h_0$ in $\mathfrak k$, so this already shows that $K/K\cap Q$ and $K/Z_K(h_0)$ coincide up to covering.