All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.

There are conditions that must be met when slaughtering animals or poultry, dabihah, in order for their meat to be considered lawful. Some of these are: cutting the windpipe and the esophagus completely. However, if any part of them remained uncut and the animal died then its meat is unlawful. Similarly, if the animal was kicking and the uncut part of the windpipe and the esophagus were re-cut, then it is considered dead meat unlawful to eat.

Kicking violently and blood gushing out, after the windpipe and esophagus are being cut, are signs of the animal`s stable life, which is a condition for the meat to be considered  lawful to eat.

According to An-Nawawi, "The Islamic form of slaughtering involves cutting the windpipe and the esophagus completely, which is the correct opinion of the Shafie School……Our fellow scholars said: "If any part of the windpipe and esophagus were left uncut and the animal died then its meat is unlawful. Similarly, if the animal was kicking and the uncut part of the windpipe and the esophagus were re-cut, then it is considered dead meat unlawful to eat." {Al-Majmou`, v.9 pp.86}.

Based on this, if you (Asker) are certain that you have cut the  windpipe and esophagus from the first time, then the form of slaughtering is valid and the meat is lawful to eat, and that some veins remained uncut doesn`t render the meat unlawful to eat.

However, if you haven`t cut them completely from the first time, then those chickens are considered dead meat unlawful to eat and re-cutting them doesn`t make their meat lawful. And Allah the Almighty knows best.