I don't play Elder Scrolls so I had to dig this up.

Flame atronachs are apparently elemental daedra (divine beings who are not ancestors of human beings, unlike the aedra), summoned through Atromancy. Apparently they are able to make their own decisions, so they have agency, so consent applies to them.

But I couldn't find how much the conjuration process removes their agency; if they're forced to obey the conjurer's orders to the letter, if they can creatively interpret those orders, or if it's a single order.

What if they consented being my magical slave because they were into it

Just because they can be summoned, doesn't mean every one you run into has been. They exist outside of being conjured. That said, I think if it has been conjured, no it cannot give consent until the spell wears off. If I recall correctly, even if you hit them, they won't attack you while summoned. I'd say that is a pretty clear indication that they cannot decide for themselves while under the effects of the spell.

But that doesn't mean you can't find one out in the wilds and "befriend" it the old fashioned way, without magic, in which case yes, it likely has the intelligence and autonomy to consent. Which really makes the spell to conjure them pretty fucked up in itself...

Is a conjured magic elemental even a person? Does it have free will? Can it comprehend and give consent in any more meaningful way than a sex toy can?

I would say no, at best they are an employee.

I would like to take up an otherwise unrepresented position in this debate and request to be an atronach.

Does consent even matter if it's not alive? It's made of fire. Do you ask a campfire before you roast a marshmallow?

They're daedra, who cares