[jcassity]

craig,
go to lowes, electrical section
purchase an "ugly's".
its a yellow book with read binder, fits in your back pocket.

its the NEC in small format.

Google NEC table 310.16, takes you down to 18awg.

always use "in raceway" or cable tray/wireway tables for doing things like this.  you are not a "free air" application.

your wire you chose had an insulation data sheet or it says info on the wire itself. 
If you wire has no information on it, its not UL or even UR.

You said "stranded" wire....
stranded actually means a single hard to bend conductor (like on my xfrmr these are all stranded / single)
Stranded is also where you have several stiff wires inside the same jacket,, like household Romex.
anytime "stranded" is used, it means a single or multiple hard to bend conductors.
Most of the time this type of "stranded wire is used in THHN/THWN applications.

"flex" or most correctly stated is RHH/RHW is multiple iddy biddy tiny hairs of copper.
you find Flex inside small lamp chord, your car battery cables, welding wire, think tiny hair

you will notice that even in Cat3 or 4 or 5 network cables,, the individual conductors are SOLID/Stranded indivdual conductors for the white/blu, org, grn, brn.

You wil noticce the cat 6 wiring when you skin back each conductor jacket,, it consists of a stress relief member plus individual tiny copper hairs that all combined equal 26 or 24awg.

so........... more visually put......
grab a hand full of straws, each straw represents a "STR" "stranded" application.
your hand represents the jacket/insulation.
notice the air gap in between each straw.  This air gap is unavoidable in an "STR" wire type because you have multiple stiff "STR" conductors adding up to equal the AWG.

Grab a hand full of those little plastic coffee stir sticks *but* the same overall bundle diameter as your straws you did earlier.
-you just sucessfully upgraded your wire by reducing the air gaps by adding more coppper.

in stranded wiring the circular millimeters of copper for 18awg is 1620 cmil

The same 18awg wire in flex has more copper and less air gaps making it the chosen wire Telcom / Power plants use.
The NEC doesnt want to say the ampacity limits on Flex , its inception was based on the assumption STR wiring would be the worse case minimums requried to meet the application.

everything 99.0 % of people deal with is 0-2000volts.
Having said that, the NEC table 310.16 gives you insulation temperature application and desired ampacity, with that you scoot to the left side of the table and it tells you what is "recommended".

Flex is more expensive,, now you just found out why, it has more copper, more valence electrons to exchange, more conductivity, more ampacity,, therefore at tad special in a way and thus a tad more expensive. 

In your home breaker panel, your main breaker (without me looking) is more likely to be STR or Stranded Stiff wire.
its cheaper... Its common, People like to do what other people do, People want cheaper,, very few uncommon people!,, unlike yourself.

i could have just said "your good to go" but thougth i would babble.