Can the Dispatcher spend actions to allow others to knowledge transfer?
No. This is not a legal action.
The Dispatcher's two abilities are:


Move your fellow players' pawns on your turn as if they were your own

Move any pawn to another city containing a pawn for 1 action



The rule book has a very specific wording for each action. The actions Drive (or Ferry), Direct Flight, Charter Flight, and Shuttle Flight all use the word &quot;move&quot; to explain what you do during that action. All of the others, including Share Knowledge, do not. These actions do not deal with moving, which is all the Dispatcher is allowed to do to other pawns.
Or more simplistically, the rules state specifically:

The Dispatcher may move other player’s pawns on his turn (using any of the available Basic actions) as if they were his own pawn. He may also spend an action to move a pawn to any city that contains another pawn. He may only move other players’ pawns if they permit him to do so. Note: For the Charter Flight action, the Dispatcher must play the card corresponding to the current location of the pawn he wishes to move.

The Basic actions only include the four I mentioned above, plus Pass. You cannot spend an action to allow other players to trade cards using the Dispatcher; Share Knowledge is a Special action and outside of the Dispatcher's abilities.