Secrecy determines whether allies receive the warning

Would the United States share the Kido Butai sighting with friendly navies?

Only if Roosevelt disclosed the sighting; a secret American ambush plan would probably keep the intelligence from being shared.

Whether friendly navies received the sighting intelligence would depend on Roosevelt's decision. If the president publicly announced the approaching Japanese force, allied governments and navies would naturally learn of it. If he kept the discovery secret to preserve an American trap, the information would probably remain compartmented. Ordinary liaison channels could not be used without risking the ambush plan.