The only minorities ensured specific rights are Kurds, who have a federal region in the north, and speakers of Syriac, who it says are free to educate their children in the language.
That isn't exactly what it says:
"This constitution guarantees the Islamic identity of the majority of the Iraqi people, as well as complete religious rights for all individuals to freedom of beliefs and religious practice."
"Iraq is a multi-ethnic and multi-religious country and it is part of the Islamic world, and the Arab people in it are part of the Arab nation."
"The Arabic language and Kurdish language are the two official languages of Iraq, and the right of Iraqis to educate their children in mother tongues such as Turkmen and Syriac in government teaching establishments ... or any other language in private institutions is guaranteed."
The right of religious freedom is guaranteed for all minorities. Also, there is a right to state education in "mother tongue" languages, of which Turkmen and Syriac are given as examples. It is not a comprehensive list.
As I said, this sounds pretty good on paper. But much depends on the fairness of its implementation.