Dragunity Aklys's effect should trigger when it's sent to the Graveyard (when equipped to a monster), but that's happened numerous times now in various situations (monster destroyed, monster synchro'd, etc.) and Aklys's effect doesn't activate. I've lost a couple of duels because of it.
Also, I had Dragunity Knight Ascalon equipped to Dragunity Arma Leyvaten, and Leyvaten was destroyed, but it didn't give me the option to summon Ascalon, and I lost as a result.
Am I dueling wrong, or are these actual bugs? It'd suck, because I happen to like the Dragunity deck a lot. :p
Read your cards carefully.
Also, the reason Alkys effect doesn't trigger when you synchro (I tested this too, it doesn't work) is because the monster is either destroyed before or at the same time as the equip; so the condition "while equipped to a Dragunity..." is not fulfilled.
Read your skills
because your enemy had jinzo so it cancels your spell cards