Electrify Flying Press does get the Electric+Flying coverage matrix. Just like regular Flying Press's coverage matrix, these types have no overlapping weaknesses, but unlike the standard coverage, they do have overlapping resistances:
x2 damage to Water, Flying, Bug, Fighting
Standard damage to Dark, Fairy, Fire, Ghost, Grass, Ice, Normal, Poison, Psychic
x½ damage to Dragon, Rock, Steel
x¼ damage to Electric
x0 damage to Ground
Yes, this means that using Electrified Flying Press against a Magnezone will result in a 1/8 type multiplier...or an 8x multiplier if you're in an inverse battle.
Since Electrified moves are super effective against Water anyway, Freeze-Dry will typically behave no different to Electrifying any other ice move. Water/Ground types like Quagsire will still be immune. If you're playing inverse battles, however, Freeze-Dry is super effective against Water no matter if you Electrify it or not, whereas Electrifying any other Ice move would turn it into a resistance. The main difference Electrify would make in this case is that if you hit a Volt Absorb user like Lanturn, the ability would make them immune, instead of taking super effective damage.