If the acceleration of a body is constant in a given reference frame, is it necessarily constant in all other reference frames?

It is not necessary that if the acceleration of the object is constant in one frame of constant then it should also be constant in other frame of reference too because the other reference frame could be accelerating relative to the object.
If there are two reference frame say and , and the reference frame are accelerating with respect to each other, then it is possible that an object moving at constant velocity with respect to frame say is accelerating with respect to frame .