Wouldn't Briarthorn trigger this thing twice when Evoked? Once for entering the battlefield, then immediately again for leaving the battlefield. And you get a sweet growth effect for another creature to go with it.
If you stack the triggers right, you could put the +3/+3 on the Pelt Collector and swing for 6 on turn 2.
Every card in the cycle is very strong when flipped. This actually could be the strongest. The biggest problem is in getting this thing flipped. Three spells in a turn is a lot to ask, especially in a deck that empties its hand as quickly as Red usually does. I don't think Ramunap Red wants this, but if a R/X variant with cantrips comes into being, maybe it would.
I have a Modern Soulflayer deck, so I am used to jumping through hoops for my double strike. This however just doesn't have enough payoff to be worthwhile. I doubt this makes the 23 in Dinosaur tribal Limited most of the time, and never in Standard.
Cartouche of Strength is a limited star and this is basically the same, but it trades Trample for a potential cost reduction. This is prime Green removal even if you aren't playing any Dinosaurs. It is potentially Standard playable in Dinosaurs. Good card.
Seems extremely narrow, why not use a card that gives a spell flashback or just simply return the card from your graveyard back to your hand?
Flashback is only for instants and sorceries. As for returning to your hand, you can only get so much use per card (Wander in Death) unless the template is broken. This is the same template as Yawgmoth's Will (Restricted in Vintage), narrowed to just cycling, but on an artifact instead of a sorcery. This is probably nowhere near Yawgmoth's Will, because there is no cycling equivalent of Dark Ritual/Lion's Eye Diamond, etc. but that won't stop brewers from trying to do dirty things with it.