Is it permissible to allocate a portion of Zakat funds to an account for the new children's cancer hospital building project in Egypt, and would this be considered an ongoing charity (Sadaqah Jariyah)?

It is not permissible to build hospitals and schools or pave roads using zakat (definition) funds, because the recipients of zakat are specified in the verse: "Zakah expenditures are only for the poor and for the needy and for those employed to collect [zakat] and for bringing hearts together [for Islam] and for freeing captives [or slaves] and for those in debt and for the cause of Allah and for the [stranded] traveler." As for donating to build hospitals voluntarily, it is an ongoing charity for which its giver will be rewarded.