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.
I have played most of my games in PVP as Dragunity (unfortunately) but I have never dabbled in those two cards. I did some testing just now.
You are supposed to use Dragunity Senatus to search for Alkys, then if a Dragunity card you control is going to be destroyed, you can discard Alkys to protect your Dragunity. You can even "@@@" one of your weaker Dragunity's into opponent, then use Senatus effect to discard Alkys to @@@ their monster. I equipped Senatus with Alkyls and Mokuba level 40 refused to attack me.
I did a search, Dragunity Legionaire also combos with Alklys, have a look.
Leyvaten, I didn't get a chance to test, but it does say "When this card is SENT to the GRAVEYARD by your OPPONENT'S CARD EFFECT" which are somewhat stringent conditions; test this against some legendary duelists and lmk what you find!
Word to the wise, Dragunity players typically build a deck around Senatus or Dux (you don't need 3 of each, but at least 3 of one of them)
Read your skills
because your enemy had jinzo so it cancels your spell cards