How would I say "the best of the best?" in terms of use as a motto for
a military unit?  I need something regal, so to speak.  I have found
optimus maximus but I am sure I do not know the proper way to decline
the words.  Thank you to anybody who could help.

Hello.

This really depends on what gender you want to use.
 
A Boy Scout troup in Louisiana use "Optimus Optimorum."

"The motto of Troop 6 is Optimus Optimorum ? the Best of the Best"
source: LCPA.org - Louisiana Boy Scout Troop 6 - July Calendar
http://www.lcpa.org/July.pdf

The problem with that, though, is that "optimus" is masculine singular
while the   the Latin word for a troop or brigade is legio (legion)
which is actually feminine.  So it does sort of raise the question:
"The best what?"  In other words, what is the masculine singular thing
that is being referred to by "optimus"?

For feminine words, "optima optimorum" and "optima optimarum" are used
to convey the same meaning.
"Optima Optimorum" (describing a hotel)
http://www.prinzess.de/
"...sell your province as the "Optima Optimarum" of provinces."
http://www.scs.k12.tn.us/STT2000_wq/9-12/hardinb/process.htm


The neuter (no gender) singular would be:

"Optimum optimorum
The best of the best"
source: Comparedefinitions.com
http://www.comparedefinitions.com/finance/optimum-optimorum.html

So what's the best approach?

Assuming that the military unit is mostly male, personally I'd go with
the masculine plural "optimi optimorum" - "the best (men) of the
best."

Indeed, that appears to be the closing motto on a web page about B26 marauders.
"OPTIMI OPTIMORUM!"
http://www.b26.com/page/historical_marauder_firsts.htm

----------
search strategy:
"of the best" optimorum
etc

I hope this helps.