Is it permissible for you to accept Zakat funds, despite your lineage being Al-Khalidi Al-Makhzumi, and your mother’s lineage tracing back to Ja’far Al-Tayyar (may Allah be pleased with him), and given your dream vision of the Messenger of Allah (peace be upon him) where you said: "Indeed, my grandfather is the Messenger of Allah (peace be upon him)"?

Zakat (definition) is forbidden for the Household of the Prophet (Ahl al-Bayt), i.e., Banu Abd al-Muttalib, based on the Prophet's (peace and blessings be upon him) saying: "Indeed, charity is not befitting for the Household of Muhammad; it is but the dirt of people." This prohibition is due to their honorable status and to keep them untainted by the "dirt of people" (charities).

However, if their other sources of income (such as the one-fifth of spoils of war) are cut off or non-existent, and they are in need of money, then it is permissible, rather obligatory, to give them zakat. They are more deserving of it than others. This is the view adopted by some of the Salaf and preferred by Sheikh al-Islam Ibn Taymiyyah and Sheikh Ibn Uthaymeen.

As for lineage from the mother's side, it does not prevent one from receiving zakat, because the legal rulings related to honor and lineage are determined by the father. A child follows his father in lineage.

Therefore, if you are from the Household of the Prophet and eligible for zakat, it is permissible for you to take from it, especially since you are not given from the one-fifth (khums).