As-salaam,
Is it permissible for our family (5-6members) to give our all zakat Fitr to one poor person?

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and messenger.

It is permissible to distribute Zakat-ul-Fitr among a number of poor people, and it is permissible as well to give Zakat-ul-Fitr of many people to one poor person.

Shaykh Muhammad ibn Saleh Al-'Uthaymeen said in As-Sharh al-Momti': "It is permissible to distribute Zakat-ul-Fitr among a number of poor people, and it is permissible as well to give Zakat-ul-Fitr of many people to one poor person."

Allah knows best.