This is a great question that unfortunately doesn't have a canon answer. The alphabet doesn't have any known or confirmed order; it may not necessarily have an order at all.

Below is the Prima Games alphabet listing. It really can't be discerned if this is the alphabet's "actual" order or if it's ordered this way for convenience. Something to note is that the "unique" characters are listed in the order they are mapped in the font: "aa" is mapped to 1, "ei" is mapped to 2, "ii" is mapped to 3, etc.

When discussing the alphabet, the runes for "aa," "ei," etc. should be counted as their own letters.

Again, it's impossible to say if the above is the alphabet's "actual" order or if it's ordered that way for convenience. The latter seems much more likely considering that the characters "aa," "ei," etc. are listed separately from the rest of the alphabet. Dragons wouldn't have any natural reason to think of these runes separately from the others.