"The small Egyptian animation production was mainly due to the Frenkel brothers", says Giannalberto Bendazzi's Cartoons (2006 edition) in its overview of 1930s animation. Most of the information in this post is lifted from Bendazzi and this comprehensive article, courtesy of the Historical Society of Jews from Egypt.
Herschel, Shlomo (Anglicised as "Salomon" in Bendazzi's book) and David Frenkel were born in Jaffa, Palestine, to parents named Betzalel and Gnissa. The HSJE article gives an account of the family's flight from Jaffa to Cairo:
Betzalel created there a bookshop and tried to live of trading, printing and binding books until the Turks came into the First World War. In November 27th 1914, the Turkish expelled from Tel Aviv the Russian Jews suspected to become enemy spies. Compelled at another exile, Betzalel and his family counting then six children were deported to Alexandria, Egypt.
The brothers were inspired to become animators after watching Felix the Cat cartoons, and they came up with a series star of their own: a fez-wearing character named Mish-Mish Effendi. The character made his debut in the 1936 short Mafish Fayda (Nothing to Do); later shorts starring the character include National Defence (1940) and Bilhana Oushefa (Enjoy your Food or Bon Appétit, 1947).
According to the article linked to above, the character got his name because a skeptical producer said that he would back the brothers' work "bukra fil mishmash" Literally meaning something along the lines of "tomorrow, there will be apricots", this phrase is apparently equivalent to "when pigs fly".
These publicity images for Bilhana Oushefa place a lot of emphasis on the character of the dancer; judging by the (very low-quality) stills below, she was live action for at least part of the film.
David Frenkel later moved to France and made cartoons about a character called Mimiche - essentially Mish-Mish in a different hat.
Some of the Mish-Mish cartoons were posted on YouTube, but removed after a copyright claim from the Frenkel family. Writing on one of the shorts, Milton Knight notes that is is partially pirated from a pair of Van Beuren cartoons, while Jerry Beck comments on "the crude animation, which I find entertaining; strangely hypnotic and bizarre, in a good way."
Jerry Beck would comment again on the series:
The character was the star of a popular Egyptian cartoon series of the 1930s by the Frenkel Bros. – who apparently were so taken with American cartoons they literally traced animation, character designs and ideas directly from them. This one, National Defense, is a World War II epic presented in two parts. In the musical first half, the animators borrow from Bosko and Buddy, mix belly dancers and dancing hooka’s, and possibly the worst caricatures of Laurel and Hardy, Eddie Cantor and Charlie Chaplin you’ll ever see. The second half takes place on the battlefield and it’s probably the funkiest animated propaganda ever made. The crude animation only adds to the charm. No matter what you think of Mish Mish, they don’t make ‘em like this anymore!