Source: Tafsir al-Ahlam al-Kabir (Ibn Sirin)
The kitchen in a dream indicates the servant of the house, the manager of its affairs, or the man's wife. Its cleanliness indicates the righteousness of the servant or wife, and its dirtiness indicates the opposite.
Source: Ta'tir al-Anam fi Ta'bir al-Manam (Al-Nabulsi)
The kitchen indicates the place of sustenance and livelihood. A lit fire in it is sustenance and fertility. If it is empty of food, it indicates poverty and unemployment.
Source: Al-Isharat fi Ilm al-Ibarat (Ibn Shahin)
The kitchen is interpreted as the head of the house. Whatever food is seen in it indicates sustenance and goodness. A spacious kitchen indicates abundant sustenance.