Can an instructor ask students to write a letter of recommendation for them (the instructor)? I am considering applying for two new jobs. I love where I am now, but these opportunities would be better for me as they would come with higher compensation and are closer to where I live. One idea I had was to ask a couple of my best students to write a letter recommending me for these positions. Is that ethical? I do not need them per se (I have others I can ask), but I was wondering about this idea. It seems like this school is looking for student-centered instructors, so I thought this might be a way to set me apart. Thoughts?
As others say, there are good reasons not to get reference letters from students: they are biased to please you, don’t know how to write references, and it might be perceived as cherry picking (you’re in fact an awful teacher but one or two students like you). 

If you want to offer insights about what students think of you, why not use your teaching evaluations? If you’re indeed an excellent educator, this should reflect in your evaluations. It’s also acceptable to offer snippets from written course evaluations: while this is still a bit of cherry picking, at the very least it’s unbiased. However, I would check your institution’s policy regarding this practice. Some universities are ok with it, others may not be. 

Finally, if you want to show you’re a great educator l suggest indicating how you go the extra mile: participating and organizing student events, mentoring, volunteer work etc.

Good luck!