The flowers themselves can be planted, just like any other harvestable. If you have a Green Thumb Sim, you can start up a Death Flower Farm. The Death Flower will die after it's first harvest (of one flower), but a Green Thumb Sim can revive the plant for a second harvest (of one flower) before the plant becomes barren. Alternatively, if you have Dragon Valley AND the Ren Faire, you unlock the Black Armored Dragon. The Black Dragon's special ability is to summon death flowers, so you don't have to farm or go looking.
Thank you for bringing back a fond Sims 3 memory that has to do with the death flower I learned that no, you don't try to 'throw' the flower at the Grim Reaper, let it play out and he'll take it. LOL!
It's great that your Sim picked the flower on his own, I've never seen that happen in any of my games. I wonder if it has something to do with one or more of his traits? He must have known that the flower would be very valuable (a life saver).
This game can never get old, there's so much to learn and experience with our Sims.
Does your sim fish? Often my sims will get a death flower while fishing.