All perfect praise be to Allah, the Lord of the Worlds, and may His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions.
Eating from a vowed animal sacrifice is impermissible according to our Madhab (Shaffii school of thought) although disagreement does exist in some forms of this Madhab and jurists of other Madhabs such as the Maliki`s who permitted eating from it in all cases save if it was allocated for the poor.
In our Madhab, impermissibility is the correct opinion since offering an animal as a vow should only be for the sake of Allah, and this kind of offering doesn't permit the vow-maker nor his dependants to eat from it. Ibn Al-Haythamy (may Allah have mercy on his soul) said (what means): "It is impermissible to eat from vowed animal sacrifice allocated to the poor, animal sacrifice due on a Muslim or Mujazah vowed animal ( a vow made for an averted harm or for a grace)." [Tohfaat Al-Mutaaj 9/363].
Moreover, commenting on the view which permits eating from a vowed animal sacrifice, Al Imam Al-Ramli (may Allah have mercy on his soul) said (what means) : "In general, the Shaffii Madhab forbade benefitting from vowed animal sacrifice at all, as is the case with Zakah and expiation [Asna Al-Matalib 1/545]. For further details, kindly refer to [Al-Majmooa' 8/417] [Hashyiatt Al-Dasookee A'la Al-Sharih Al-Kabeer vol. 2, pp.90]. And Allah Knows Best.