In this paper, we combine methods in \cite{DB} and \cite{KPT} to compute
universal minimal flows of groups of automorphisms of uncountable
$\omega$-homogeneous graphs, $K_n$-free graphs, hypergraphs, partially ordered
sets, and their extensions with an $\omega$-homogeneous ordering. We present an
easy construction of such structures, expanding the jungle of extremely
amenable groups.