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I think it's state/institutional specific. I'd check into the schools in which you're looking to get a teaching position. I have seen (residing in NY) LPN's teaching LPN clinical, but I'm not sure about CNA courses or MA courses. Your best bet is to look at the requirements for these jobs, speak with HR, and then make your choice from there.
I think for phleb, you have to be a CLS (clinical lab scientist), which is a totally different route in school than LPN/LVN, but that's just based on my own phleb education. Considering that nursing schools now have NO phleb requirement, I doubt it would be legal for any kind of nurse to teach phleb for certification. I would also imagine it being harder to line up phleb externships as a LPN, since you'd likely have few lab connections.
CNA and MA, I would imagine it'd be fine. I have a LVN friend here in CA that teaches CNA through a for-profit school.