Question

Can Pokemon found with the help of dex nave have more than 1 egg move?

Answer 1

Yes
But in order to get more than one egg move, you need to continuously use the DexNav until you reach a high search level (which can be seen in the top-right corner of the DexNav while searching)
It's kind of like chaining with the PokeRadar, but just with a different device
Hope I helped~
Source

Answer 2

I believe it will depend on how many moves any given pair can pass off to their offspring, as opposed to a "dex nave"