Recommended way to load (non-interactive) animations (made using Maya) into OpenGL ES on iOS and Android

Well, OpenGL(-ES) itself is just a drawing API, it doesn't do anything related to animation. Animation playback is managed by a own animation system. The output of such a system are transformation parameters, that you can later use to place and deform geometry when drawing with OpenGL. The usual approach to this these days is a skeletal animation system, i.e. you add some skeleton to the model, where each vertex is bound to a set of bones, with per vertex-per bone weighting. Bones can be represented as a combination of a translation and a quaternion. The translation usually is a constant, so what the usual animation system gives you is the vector of quaternions describing the skeleton pose. This you load into a uniform (a vec4) or a GL_RGBA32F 1D texture with the width being the number of bones, which is used in the vertex shader to apply per-vertex transformation based on the pose. The vertex-bone weights usually are submitted as additional vertex attributes.