I sincerely doubt the item is a flashlight. During daylight and with multiple lighting sources directly on the stage, he wouldn’t need one. If he did it would be in his pocket instead of “taking up one hand to assist Hillary”.
No, it really is a flashlight.
You can see the light reflect off the left sleeve of the guy in the dark gray suit, just above his elbow, in this video:
https://gfycat.com/OddUnitedAmericanratsnake