What are the steps to do an Intra-Post Transfer so that I can deploy? What are the chances of getting it approved?

Start with your NCO support channel and determine whether you current unit is willing to lose you. If not, your request will probably be dead in the water unless the deploying organization is severely short your MOS and grade. If they are willing to release you then see your S1 to submit the paperwork. If they are not willing to release you, request to see the Bn CSM and be prepared to execute a decision brief where you lay out both the positive and negative for you deploying. It probably won't change his mind but it might. If it doesn't you can still request, your unit can still recommend disapproving, and you will probably make some personnel in your Chain upset.

CPL(P) (Join to see)
So a few things......you may be doing the BN level CoC a favor by asking. Deploying units are often baclkfilled open critical slots with members tasked from other on post units. For all you know there is a Wheeled Vehicle Mechanic slot needing filled but no one has so far wanted to put a name to it.

Point is, start easy, let your CofC know your interested.......If they say no..
You have options, none of them good, but the end result may end up being you deploy.

No leader likes having an and run done on them..If you ask and are told no, if the no is justified at the CO level, yet you go to the BN CSM and they see a bigger picture and say yes,,,you'll deploy....You may remain on the books in your current unit, and return to that same unit when you get back. Promotions ect are in the hands of your designated unit.
You could find out the two company commanders are friends, and you deploy only to be tasked to fill some crappy job that someone has to be tasked to......and you fit the bill.

Lastly You WANT to deploy? Having done so a couple of times, I can say for certainty there is nothing gained worth what you loose.

Ask the company 1SG, be ready to say why you want to deploy. If you convince the 1SG its for the right reasons, and there is a valid need, likely you will go.

The first thing you need to do is talk with your CoC, starting with your team leader. Don't go around your CoC. That's a quick way to get on their bad side.