What brand flat wound string will fit correctly on an Alembic Essence mid-scale (32) bass?

On my 32 Series One I use Thomastik-Infeld Electric Bass Nickel Flat Wound Roundcore 4 String 32 Scale, .043 - .106, JF324

Because the two-piece bridge and tailpiece assembly adds about two inches to the scale length, 34 strings will fit fine. Thomastiks have very little tension compared to other flats, but have a unique and incredible tone once they're settled in.

What tone are you looking for?  Any regular long scale string should work.  I haven't listened to the TI, though many swear by them.  
 
LaBella makes a nice string if you're looking for a very dead, traditional flat wound tone.  
 
Chromes are a great choice if you're looking for an almost-round tone with less finger noise.  That's what I use and I find them very versatile.

Hi Rick; welcome to the board!

+1 on the Chromes. I have a set of their medium scale 45-100 on my 32 Distillate and they fit perfect.  (String code - ECB81M)

I have the chromes on one bass, and the TI flats on another, and personally I prefer the TIs.  I've also tried Rotosounds flats, and they were very nice as well, somewhere between the two both feel-wise and tonally.  (and I'm a Roto hater, normally...)

I've also been using the DR flats and they are very nice. Not quite as bright as the TIs with a little more fundamental. Not as high tension as the Chromes or La Bellas.
 
Edwin