What is the proper protocol for applying to a postdoc sponsored by an one's undergraduate adviser? I am finishing up a PhD in Statistics in the United States and am currently applying to postdocs. My undergraduate studies were done in a top 5 institution in Statistics; my grad school is top ~25. I saw that my undergraduate thesis adviser is looking for a postdoc, and it seems like a great fit with my research interests. 

What is the proper protocol to apply for a postdoctoral position with a professor with whom you already have a working relationship? Would it be appropriate to send them an email to indicate my interest in the position (along with say a cover letter and CV)? Wording this email has been a little difficult, as I'm trying to avoid sounding like I'm leveraging my connections with them to get this position. Is applying to a postdoc sponsored by a former adviser something that one should avoid doing? What else should one take into account in such situations? 

For more context, I have been keeping up with this professor, but not extremely closely (we send each other a few emails a year just to catch up). This person supervised my undergraduate honors thesis and supported my application to graduate school.
I would suggest that you apply in the normal way, just as anyone else would. There may be rules for how that is done and you have to be attentive to them. Provide all of the required materials and make your best case for your application. 

But you can, in addition, send the professor a simple "heads up" email that you are interested in the position and are applying. Don't try to make your case in this email. Do it in the application materials. 

If you didn't have a previous relationship with the prof that you have maintained, such a letter would be presumptuous and ignored or treated as an irritant. But in the case at hand it would be a normal thing. 

You aren't taking advantage, exactly, since you have no control over the process.