Is it possible to get a slot to reclassify to 31K?

As a reclass, be prepared to wait a while. It's hard enough to get a slot when enlisting in the first place and out of my class of 24 right now (biggest class they've ever had btw) there's only 4 inserts and one of them is NG. I just got lucky and hardballed my recruiter saying I wasn't gunna join till a 31K slot opened up and waited till it did. They can't save slots for this MOS, theres either a slot open when they look or there isn't.

First, your Career Counselor is the person you reclass through, if they say there are no slots, then you can't reclass into that. I haven't seen any slots since they first created the MOS years ago and only 31B were allowed to reclass into it.
Second, 31K is not an application MOS as other people suggested. There's no packet for it, the slot exists or it doesn't. HRC holds the majority of training seats for IET students and only a few go to prior service.
Your Career Counselor is the subject matter expert when it comes to reclass. I would avoid asking the internet because you'll get a lot of misinformation and straight bad data. It's a highly technical area and the seats change daily. If you feel your counselor isn't telling you everything you can go to the Senior Career Counselor at the brigade and ask them.

There’s actually a Mil-per message out for this mos right now if you look on HRC. It’s open to applications.

If you want to know what you need for your reclass packet I will be more than happy to help you.

I just reclassed to 31k in January, I had to wait 3 months for a slot and I got lucky enough to get one. Reclass slots for 31k are rare (due to there only being a handful a year) ,but there is no harm in trying. Maybe you could get lucky like me and get a slot. My school date isn't untill March 2019 ,but as I said even getting a slot is very very difficult, but not impossible. If you do decide to peruse it just be prepared to wait a long time and your school date will be atleast a year out.

You do have the ability to reclass. I would get your packet ready and drop it soon or in the next few months. 31k mos is projected to loose up to 40% of current E5 sergeants this year alone.
As far as the packet and how to do this process, I am not 100% sure. I would point you in the direction of your career counselor, however he seems to not know much either. I will do some asking around and see if I can find anything for you.

Yes it is, it just requires alot of patience and persistence on your part. I reclassed to 31K in January, I had to wait 3 months before a slot opened, and it took me calling retention every say for those 3 months to get it.

You can reclass but you have to go through the MP course as well as the basic k9 course. Although I've been told by my ncos they won't accept anyone who is an nco. Only specialist and below. It's hard to get especially if you have to go through the MP course as well. It's easier so current mps to get it.