How do you make a flying squid?
/summon Squid ~ ~ ~ {Riding:{id:"Bat"},Invulnerable:1}
This summons an invincible squid riding a bat. The invincibility means the squid can't airdrown but the bat can still be killed.
If you want it to never despawn:
/summon Squid ~ ~ ~ {Riding:{id:"Bat"},Invulnerable:1,PersistenceRequired:1}
To name it Derp, you'd need:
/summon Squid ~ ~ ~ {Riding:{id:"Bat"},Invulnerable:1,CustomName:"Derp",PersistenceRequired:1,CustomNameVisible:1}
This is too long for the chat box however and it might be simpler just to spawn a Nametag and use that.
UPDATE: I took some info from the other answers and made this:
/summon Squid ~ ~ ~ {Riding:{id:"Bat",Invulnerable:1,PersistenceRequired:1,ActiveEffects:[{Id:14,Amplifier:-10,Duration:2147483648}]},Invulnerable:1,CustomName:"Derp",PersistenceRequired:1,CustomNameVisible:1}
Persistent invincible squid named Derp riding a persistent invisible invincible bat.
Fly my pretties, fly!
A true flying squid would something like this, I think:
/summon Squid ~ ~1 ~ {CustomName:"Derp",CustomNameVisible:1,Invulnerable:1,PersistenceRequired:1,Riding:{id:"Bat",Invulnerable:1,PersistenceRequired:1,ActiveEffects:[{Id:14,Amplifier:-10,Duration:2147483647}]}}
Named, Invulnerable, Persitent, flying an invisible bat.