Am I permitted to use a portion of my Zakat to pay off the debt of an insolvent person?

The zakat on wealth must be disbursed in the country where the wealth is located. If your wealth is in Egypt, disburse it there. If it is in your place of work, disburse it there. If some of it is here and some there, then disburse the zakat for each portion in its respective country. It is permissible to transfer it out of necessity.