  We define a projective Fraiss\'e family whose limit approximates the
universal Knaster continuum. The family is such that the group
$\textrm{Aut}(\mathbb{K})$ of automorphisms of the Fraiss\'e limit is a dense
subgroup of the group, $\textrm{Homeo}(K)$, of homeomorphisms of the universal
Knaster continuum.
  We prove that both $\textrm{Aut}(\mathbb{K})$ and $\textrm{Homeo}(K)$ have
universal minimal flow homeomorphic to the universal minimal flow of the free
abelian group on countably many generators. The computation involves proving
that both groups contain an open, normal subgroup which is extremely amenable.
