This is a reproduction of a page from "one of the Egyptian magazines" (not further identified) from the area, with some of the suggested designs:
Many of the designs are derived from the red-white-black tricolor that originated with the Arab Revolt against the Ottomans and was increasingly used for Arab flags; some combined it with he Royalty-era colors, not always successfully.
In the end, the first flag chosen for the Egyptian Republic was a simple Arab tricolor with no other decoration (left). Except for slight differences in shape, that flag is essentially identical with the one Yemen uses today.
Somewhat later it was decided to add the "Eagle of Saladin" (an earlier version of the eagle on today's flag) and the old royal emblem.