Keep in mind that without a FIRE monster in your hand, Hazy Flame Peryton cannot use its search/special summon effect. Furthermore, some monsters are better to discard from your hand than others for its effect, since the purpose of Peryton's effect is to overlay into a rank 6 Xyz monster, especially Hazy Flame Basiltrice.
Hazy Glory can return the FIRE monster discarded from your hand to use Peryton's effect if it is a Hazy Flame monster. It can also be used to normal summon Hazy Flame Peryton a second time by adding it to your hand.
If you want to abuse the effects of 3 of this card, "Volcanic Shell" can be used to add copies of itself to the hand to fulfill part of "Peryton's" cost.
By using this card's effect to discard another "Hazy Flame" monster and summon 2 "Hazy Flame Hydras" from your Deck, you can Xyz Summon either "Hazy Flame Basiltrice" or "Evolzar Solda" (as "Hazy Flame Hydra" is a Dinosaur-type monster and "Evolzar Solda" is FIRE), then attach this card and the discarded monster as additional Xyz Material, giving you either a 3300-ATK monster that can't be targeted by card effects (and can be brought to full power by the 2nd effect of "Hazy Pillar") or a 2600-ATK monster that can negate 4 of your opponent's Special Summon attempts.