Sorry, but neither I nor dictionary.com buy the "'flat' is not synonomous with 'horizontal'" argument.

Here's their definition of "flat"

1.horizontally level: a flat roof.
2.level, even, or without unevenness of surface, as land or tabletops.
3.having a surface that is without marked projections or depressions: a broad, flat face.
4.lying horizontally and at full length, as a person; prostrate: He was flat on the canvas after the knockdown.
5.lying wholly on or against something: The banner was flat against the wall.
6.thrown down, laid low, or level with the ground, as fallen trees or buildings.
7.having a generally level shape or appearance; not deep or thick: a flat plate.
8.(of the heel of a shoe) low and broad.
9.spread out, as an unrolled map or the open hand.
10.deflated; collapsed: a flat tire.
11.absolute, downright, or positive; without qualification: a flat denial.
12.without modification or variation: a flat rate.
13.Informal. lacking money; broke.
14.without vitality or animation; lifeless; dull: flat writing.
15.having lost its flavor, sharpness, or life, as wine or food; stale.
16.(of a beverage) having lost its effervescence.
17.without flavor; not spiced: flat cooking.
18.prosaic, banal, or insipid: a flat style.
19.pointless, as a remark or joke.
20.commercially inactive: a flat day in the stock market.
21.(of a painting) not having the illusion of volume or depth.
22.(of a photograph or painting) lacking contrast or gradations of tone or color.
23.(of paint) without gloss; not shiny; mat.
24.not clear, sharp, or ringing, as sound or a voice.
25.lacking resonance and variation in pitch; monotonous: a flat delivery of the speech.
26.Music.
a.(of a tone) lowered a half step in pitch: B flat.
b.below an intended pitch, as a note; too low (opposed to sharp ).
27.Grammar. derived without change in form, as English to brush from the noun brush and adverbs that do not add -ly to the adjective form as fast, cheap, and slow.
28.Phonetics. lenis; voiced.
29.Nautical. (of a sail)
a.cut with little or no fullness.
b.trimmed as nearly fore-and-aft as possible, for sailing to windward.
30.flat a, the a-sound (a) of glad, bat, or act.


Perhaps the river was named Flat River because it was dull and uninteresting. (Definition #14)

By the way, Lester's name was spelled "Flatt".