Is it possible for a Navy vet to re-enlist into the Army (specifically 11B infantry scout) and maintain rank (E-3)?

You need to talk to your squad leader and tell him. Then you Will start the process on getting your conditional release form signed and sent up the chain. It's a long process

Talk to a recruiter. Scouts are 19D not 11 series, i.e. Infantry. You may also be an infantryman or several other MOSs (13F, 11B, 19D among them) and earn the 6B ASI which is awarded by attending the Reconnaissance and Surveillance leaders Course.

http://www.benning.army.mil/Armor/316thCav/129/HWLC/content/pdf/DA%20Pam%20611-21%20Table%2012-2.pdf

Last I knew, and, admittedly, my information is a bit dated, every service provides some sort of advancement in recognition of prior service, education, etc. Best advice, in addition to speaking with a recruiter, is to get into the publications that govern enlistment.

I don't know your exact circumstances and I'm only guessing here, but if you are already separated from the USN, you will need your DD-214 and they will check your reenlistment eligibility code. If you have something other than an Honorable Discharge (i.e. a General Discharge), you might need to apply to have it upgraded. Check your RE-Code against this chart from Army.com

http://army.com/info/prior-service/re-codes-explained

Good luck it takes a seriously mentally strong individual to be a 11b scouts arnt that bad from what I hear

Do you have a college degree? Instant E-4! Anyway, keeping rank in the Army depends on how long you have been out and how close your previous job translates to your new job. You should also post your question on the go army forums since recruiters hang out there too. Also what do you mean by infantry scout? I heard of cavalry scouts 19Ds... but I think the Army eliminated many of the 11 specialties (C, H, etc). I think the LRRP units are gone too. Also why did you choose only infantry? Is it just light infantry? What about mechanized heavy infantry? Or Airborne Light Infantry? I was in two different types of infantry units (both light) but one was airborne and the other was mounted. I rarely did any cool shit, except during my deployment. One of my biggest disappointments from my infantry days was the lack of shooting opportunities. I wished everyday we could shoot every week and do field problems. Get ready to do stupid shit for no reason or stand around in formation for no apparent reason or pull security for hours as the COC contemplates the next op order. You will also hear the word frago a lot.

What about being an engineer? Combat Engineers 12Bs is a very intensive mos where you carry everything on your back and engage in the enemy but w/ a engineer twist. I went through the 12C course which used the same course as the 12B but lacked all the cool shit: using explosives, creating obstacles, etc, etc. Plus as an engineer you get to try out for the Sapper tab.

Compare it for yourself:
Infantry = https://www.youtube.com/watch?v=dY5CPb2GPgs
Combat Engineer = https://www.youtube.com/watch?v=OyoYhLKpQ-g

Should be able to keep your rank. Best thing is sit down with a Recruiter. They know all the current rules.

Didn't think you had to redo boot camp for army, they're the fattest ones

As for re-enlisting in a different branch than you originally served, I believe that question has been answered fairly extensively. On the question of being out for a period of time and re-enlisting, this I can speak to. My brother originally enlisted in 1988 and served 8 years, separating in 1996. After his discharge, he filed an application for disability and was awarded a 10% rating in 2002 for a knee problem, which has since been corrected surgically. In 2012, 16 years after his initial separation, he spoke with a Reserve Recruiter about the possibility of re-enlisting. After voluntarily ending his disability and being cleared by the Medical Review Board, he (re-)enlisted in the Army Reserve and accepted an AGR assignment, received a credit of 8 years for prior-service and he was given his prior rank of E-5 and all the awards he had previously received.

When I asked him about it, he explained that when he met with the recruiter initially, they just discussed what he wanted to do. During subsequent meetings, they discussed his experience and previous enlistment duties. Eventually, their meetings turned into more of a negotiation of sorts. The whole process took a few months, but in the end both parties were, apparently, happy with the results.

Point being, anything is possible with the right circumstances. Just go into tit with an open mind and don't be afraid to stand firm on what you want, but be prepared to compromise as well. With all the stuff happening around the world, the various branches are motivated (for lack of a better description) to sign prior service-members willing to work in certain jobs. And, with that, I wish you the best of luck with it.

FN Broc Afseth
Granted my info is a bit out of date, so keep that in mind. But I've heard of instances of prior branch (Navy in your case) going Army. Depending on how long you've been out you may not have to go through full Basic Training, but what is referred to as Operation Blue To Green. Check this out:

http://www.goarmy.com/careers-and-jobs/current-and-prior-service/continue-serving/transitioning-services/blue-to-green.html

Even if you start over at e-1 who cares? It'll only take you a year or so to get back.