Have filled in my collection of LifePo4’s pretty well—but cannot find one in 18350 size.
A quick google shows two at DX.
http://dx.com/p/soshine-rechargeable-1800mah-lifepo4-18650-batteries-black-2-pcs-156741?tc=CAD&gclid=CNeQ-I3vwLsCFYN_QgodMQIAig
http://dx.com/p/18650-rechargeable-lithium-lifepo4-battery-2-pack-1350mah-1879?tc=CAD&gclid=CJm8ooPvwLsCFe1xQgodHkgA0g
I think you could probably find more if you looked hard enough. 
LiFePO4 batteries in the 18650 size are common. I’ve even seen some 18500 solar batteries at Target. But the batteries in question here are 18350s.
I have never seen those in 18350, but 16340 does exist (also called RCR123).
AW, Soshine, Tenergy sell those.
Yes, I have common sizes in LiFePo4—16340, 14500, 18650, 26650—but 18350
does not seem to exist in this chemistry.
I guess my old eyes aren’t what they used to be, especially late at night when a 3 looks like an 8. 0:)
Not common, but they are readily available on alibaba. The trick is to find them in retail quantities.
The Alibaba post title says LiFePo4, but neither the description nor the pics
describe LiFePo4. Look like regular Li-Ion flames
Those are no LiFePO4 cells. There are Ultrafire 18350 LiFePO4 cells though, but I wouldnt trust Ultrafire with batteries. ;)
The OP asked if LiFePO4 18350 cells exist. I think the many, many vendors on alibaba claiming to sell LiFePO4 cells in a variety of sizes, including 18350, is good evidence that they do exist. But since they are mostly used in power tools and similar applications, the difficulty is finding a vendor selling them in retail quantities.
It’s hard to know for sure what the Ultrafires Trustfires linked above are, since the description repeatedly calls them LiFePO4 cells and then specifies the 3.7/4.2 voltages which do not apply to the LiFePO4 chemistry. I would guess that they are LiFePO4 and that the voltage errors are the usual chinese copy/paste carelessness with descriptions. Hard to say for sure without contacting them, but I’ll leave that chore to someone who actually wants to buy some. 