For many western listeners, film scores and other music have created a subconscious association between ancient Egyptian culture and a variety of Arabic and Gypsy scales. However, everything I've read says the most prevalent mode in real Egyptian music was what we now call "Dorian" (all white keys D to D). As an aside, the ancient Greeks actually called that scale "Phrygian" but a mis-translation of ancient Greek literature by monks in the middle ages resulted in modern musicians using different names for the diatonic scales than the Greeks did.

Anyway, the Egyptians supposedly preferred Dorian mode because it's the only symmetrical diatonic scale (half-steps are in the same relative location ascending and descending). A chart might help explain what is meant by "symmetrical":

For any other diatonic scale, the half-tone steps are in different positions in the ascending and descending scales and they are therefore not symmetrical. Let's use Ionian (major scale) mode as an example:

And why does that matter? Well, the ancient Egyptians were renowned mathematicians, astronomers and mystics, so it seems natural they would incorporate mathematical relationships and mystical symbolism into their musical structures, as they did with their architecture and other arts. The concept of symmetry obviously conforms to that aesthetic, and seven is a prime number with ample mystical significance. One source even claims the Dorian scale mathematically represents an ellipse with two foci, like the orbit of the earth around the sun. Unfortunately, Dorian mode just doesn't sound very Egyptian to me because of all those years of brainwashing by soundtrack composers.

However, diatonic scales were an invention of the ancient Greeks, defined as a seven note musical scale comprising five whole steps and two half steps, in which the half steps are maximally separated. Because western music theory stemmed from the Greek tradition, and this convention was used to design the layout of modern keyboards, a diatonic scale can also be defined as a scale that can be played using only the white keys on a piano keyboard.

So with a musical tradition independent from the Greeks (and no pianos) why would the ancient Egyptians have been constrained to diatonic scales? Dorian mode is the only symmetrical diatonic scale, but symmetrical non-diatonic scales are abundant (the most obvious example being the hexatonic whole-tone scale). We'll narrow it down a bit by assuming the ancient Egyptians preferred heptatonic scales because of the mystical connection with the number seven. So let's geek out with some math. If you assign a numeric value to each scale step based on how many semi-tones are between, then any symmetrical heptatonic scale can be represented as a sequence of seven numbers that is the same forwards and backwards and whose sum is 12. From there, it's easy to calculate all possible symmetrical heptatonic scales:

That list of numbers should be all you need to sound like King Diamond.

Just kidding. Pictures help. A lot. And I put them in order of usefulness for establishing an "Egyptian" mood in a musical piece. That order is admittedly subjective, based solely on my opinion. Everybody's ears are different, and the ones at the bottom might sound more Egyptian to you than the ones at the top. Click on the picture for an audio example.

2122212 is Dorian mode, the allegedly "authentic" Egyptian mode. 'Nuff said.
1312131 is commonly known as the 'Gypsy'scale. Hello, old friend. Decades before I did any real research into Egyptian scale modes, I was using this one to evoke an Egyptian atmophere. It's the basis for the 7/8 theme from the intro to "Temple of Seven Jackals" by Phantasm as well as the "Legacy of Alexander" riff (which first appeared in Legacy of Alexander Pt. I on The Traveler and recurs as a principal theme on Rise of Alexander).
1214121 sounds very Egyptian and ominous to me. I'm using this scale in the song "Oracle" on Rise of Alexander.
1222221 sounds Egyptian to me as long as melodic phrases avoid resolving to the root.
2114112 also lends itself to some Egyptian sounding riffs, provided the adjacent semi-tones are used sparingly. Be careful though; to me it kind of ruins the effect if you play II, III, IVb or V#, VI, VIIb in sequence.
1124211 sounds exotic but not particularly Egyptian to my ear. It can certainly be used to develop some interesting licks, though.
3112113 is another very intriguing scale that doesn't sound particularly Egyptian to my ear but could definitely be the basis for some exotic soloing.
1132311 doesn't sound a bit Egyptian to me, but it seems to have endless possibilities for soloing in other contexts. The double-flatted third and sharped sixth make any feeling of major/minor modality completely ambiguous.
2212122 is commonly known as 'Major-minor' mode. Plenty has been written about this elsewhere, and it doesn't sound very Egyptian to me.
1116111 is very chromatic-ish, doesn't sound Egyptian, and I don't find it terribly useful in general.