Devac, b_b, you're both right. Prepping an IM Epi injection isn't super difficult, and some AlS(AEMT and paramedic)providers I know say basics should already have it. Five minutes to mastery is low-balling it though.
Where the difficulty would likely arise is in training a state's worth of basics on a new skill that involves sharps and one of the more powerful meds we keep on the truck. Given the potential complications like Devac mentioned, you want to be well practiced at it. Lots of my state is covered by volunteer EMS services that don't get a ton of calls, and even fewer anaphylaxis calls. Staying sharp with your sharps can be a little difficult in that kind of situation, but it will probably be ultimately doable.