Praise be to Allah.
The presence of some blood on chicken or other meat when cooking it does not matter, because blood that is shed or poured forth is that which flows from it at the time of slaughter, and it is this blood that is haraam. As for that which remains in its veins after slaughter and comes out when it is cut up or cooked, this is not blood that was shed or poured forth, and it is something that Allah overlooks.
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said:
Eating grilled meat and steaks is permissible whether the meat was washed or not; rather washing the meat of the animal that has been slaughtered in the prescribed manner is an innovation. The Sahaabah (may Allah be pleased with them) at the time of the Prophet (blessings and peace of Allah be upon him) would take the meat and cook it and eat it without washing it, and they would see the streaks of blood in the vessel. That is because Allah only prohibited to them blood that is shed or poured forth. As for that which remains in the veins, He did not prohibit it; rather He prohibited them to seek it out in the veins as the Jews do. End quote.
Majmoo‘ al-Fataawa (21/522)
He also said:
It is only the blood that is shed or poured forth that is prohibited.
It is proven that the Companions of the Messenger of Allah (blessings and peace of Allah be upon him) used to put the meat in the vessel and streaks of blood would be seen in the water, but I do not know of anyone among the scholars who differed with the view that this is overlooked and is not regarded as impure, according to scholarly consensus. End quote.
And Allah knows best.