We consider the manifold Fln(ℍ) = Sp(n)/Sp(1)n of all complete flags in ℍn, where ℍ is the skew-field of quaternions. We study its equivariant complex K-theory rings with respect to the action of two groups: Sp(1)n and a certain canonical subgroup T = (S1)n (a maximal torus). For the first group action we obtain a Goresky-Kottwitz-MacPherson type description. For the second one, we describe the ring KT(Fln(ℍ)) as a subring of KT(Sp(n)/T). This ring is well known, since Sp(n)/T is a complex flag variety.
