In order to avoid leaving eggs as trash, keep a private notebook or digital file of where you hide all of the eggs. If you are using adult volunteers, make sure they have a private notebook or file which they will share with you. I discourage using children as volunteers as they will probably lose at least some of the eggs.

After the hunt ends, go back and pick up any eggs that nobody could find. Or, during the hunt, slowly pick up the eggs so that all are found at the end. You can have your adult volunteers help with this as well

I don't condone using a flamethrower for an Easter egg hunt, especially one involving kids. Furthermore, I can't tell you how you would obtain one and don't even know if it's possible, since in many jurisdictions they are illegal or require a special license. If you really like fire, I instead recommend hosting an Easter grill or small campfire in addition to your hunt, where the adults can cook food over an open flame or children can roast marshmallows for s'mores (though be sure the campfire is safe and legal in your area, and make sure to monitor your kids closely)
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