My friend special summons cyber jar, then uses book of moon on it to flip it down. Can he flip it up on that turn?

No. You cannont change a battle position of a card the same turn you summon it except by a card effect.

EG - Boook of Moon, Tsukuyomi, Enemy Controller, etc, etc

Alright, if that counts special summons, then I win the duel. Thank you.

It doesn't matter how it was summoned (Normal, Flip, Special).

If a monster has...

A.) Been summoned that turn (doesn't matter how)

B.) Already had an attack declared with it (whether or not it gets negated doesn't matter)

C.) Had already had its position manually changed that turn (meaning you actually change its position yourself without any effect)

...then you cannot manually change that monster's battle position that turn except by an outside card effect.

Or, in the case of Little Winguard, it's OWN effect.

I guess I should've said "card effect" in general, lol.