Bad Flier. The zombie chicken falls at the end of its turn if it's airborne and the only thing holding it aloft is its fly speed. 

Undead Fortitude. If damage reduces the zombie chicken to 0 hit points, it must make a Constitution saving throw with a DC of 5 + the damage taken, unless the damage is radiant or from a critical hit. On a success, the zombie drops to 1 hit point instead.

Multiattack. The zombie chicken uses Fluttering Presence or makes two peck attacks.

Action Melee Attack. Melee Weapon Attack: +5 to hit, reach 5 ft., # target. Hit: 6 (1d6 + 3) piercing damage. 

Fluttering Presence. The zombie chicken flutters at one small creature. That creature must make a DC 13 Dexterity saving throw or be knocked prone.