No, on a 1995 Buick Park Avenue, the transmission does *not* need to be removed to replace the starter and flywheel. The starter is typically accessed from underneath the vehicle, and while it might be a tight squeeze, it's a common job that doesn't require transmission removal. The flywheel is behind the starter, so access to it also doesn't necessitate transmission removal.
The mechanic is either mistaken, trying to inflate the cost of the repair, or is dealing with an unusual circumstance (highly unlikely given the straightforward nature of this repair on this model). Get a second opinion from another reputable mechanic. They should be able to confirm whether transmission removal is truly necessary for this repair on your specific vehicle.
