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If a model that is part of an Inquisitorial Henchmen squad gains the Scout or Move Through Cover special rule, would that be conferred to the unit's Dedicated Transport when the model is embarked?

If the dedicated transport is the models dedicated transport then yes.

A squad/model that has scout/infiltrate confers this ability onto its dedicated transport.

No you cannot put an independent character that has scout into a squad and then give it to that squads transport because it is not the characters transport.

Edit: Move through cover is not conferred onto a dedicated transport, the only way to give a transport "move through cover" is essentially giving it dozer blades.

Ok, good to know, too bad about Move Through Cover. I've already got my list down for a Kill Teams tournament now I'm deciding on what special rules to give 3 models due to the Specialists rule on Kill Team scenarios. Was hoping to give one guy Move Through Cover to make it easier on their transport.

Infiltrate is NOT conferred, however it does confer the ability for the vehicle to Outflank.

You cannot have inquisitorial henchmen in a kill team game anyways: you have no Inquisitor to unlock them.