Should I request a letter of recommendation from current employers that don't want me to leave? Let me explain in more detail... I currently occupy a fixed-term temporary faculty position that is set to expire at the end of this academic year. The position I have now will go up for a national search for a tenure-track appointment starting next academic year.

My current department head and Dean both have repeatedly expressed their desire that I apply for the tenure-track position and I intend to. However, there's no guarantee that I'll keep this position and I want to be employed next Fall. I have found another position that would be a good fit in case my current position goes to someone else (a very real possibility as my field has many qualified applicants and few jobs) and as part of their application they want current letters of recommendation. 

I know my department head and Dean both would recommend me highly, but I see a potential conflict of interest. I'm also unsure if asking them for recommendations could be perceived as a slight and I don't want to burn any bridges at my current position because keeping it would be my first choice.

Another complicating factor is that this is my first university position and all other potential references either worked with me as a student or professional colleague in a non-academic capacity. 

Any advice on the best course of action to take in my position?
Without further information, I would assume the department head and dean will behave ethically and ignore the conflict of interest.  They should understand you want to hedge against losing the competition for the tenure track position. Therefore you could use them as references.