How did the slang meaning of "flog" come about?
When you flog a horse you make it go faster. So to flog goods is to make them move faster.
Eric Partridge, A Dictionary of Slang and Unconventional English, fifth edition (1961) has this entry for flog:
flog. To whip: from ca. 1670. Until ca. 1750, c[ant]; in C19–20, S[tandard] E[nglish]. [Elijah] Coles, [Dictionary] 1676. Prob. an echoic perversion of L. flagellare.—2. To beat, excel: ca. 1840–1910.—3. In late C. 19–20 military, to sell illicitly, esp. Army stores; and in post G.W. c., to sell 'swag' to others than receivers. F[raser] & Gibbons [Soldier and Sailor Words and Phrases (1925)]; B. & P. Ex flog the clock ["move its hands forward"] or flog the glass ["turn the watch-glass"]. [Cross reference omitted.] —4. Hence, to get the better of (a person) esp. in a bargain: military: 1915. F[raser] & Gibbons.—5. Hence (?), to exchange or barter: from ca. 1920. Anon. Dartmoor from Within, 1932.—6. See flog it [the entry for which reads "To walk: military: from ca. 1912. F[raser] & Gibbons. Ex the effort {flog oneself along}."—7. (Ex [sense] 3.) 'To offer for sale (especially when financially embarrassed ...),' H[unt] & P[ringle, Service Slang (1943)]: Services, since ca. 1935.—8. To borrow without permission: Services: since ca. 1937 H[unt] & P[ringle]. (Cf. sense 3.)
Partridge does not persuasively explain how English made the jump from flog sense 2 ("To beat, excel") to flog sense 3 ("to sell illicitly")—unless you find his deriving the usage from "flog the clock" and "flog the glass" persuasive. But Partridge seems quite confident that sense 3 emerged in the late nineteenth century and had a military origin; and the emergence (in the services) of flog in the sense of "to offer for sale [under financial pressure]" suggests some underlying institutional memory of flogging in the sense of selling illicitly, from several decades earlier.
John Ayto & John Simpson, The Oxford Dictionary of Modern Slang (1992) has a much shorter entry for flog:
flog verb 1 trans Brit. orig military To sell. 1919–. M Drabble Let's go ... and look at the ghastly thing that Martin flogged us. (1967). 2 intr. and refl To proceed by violent or painful effort. 1925–. Times [Lorry drivers] are being encouraged to 'flog on' even in bad weather (1964).
Tony Thorne, The Dictionary of Contemporary Slang (1990) sems to confirm Partridge's earlier genealogy of the term:
flog vb to sell. A common colloquialism in Britain which would still be cosidered slang by some speakers. The word originally referred to selling off military stores illicitly and is said to derive from a 19th-century expression to 'flog the clock', meaning to put the clock forward to shorten the working day, later extended to other devious behaviour.
The OED says
c. slang (orig. Mil.). To sell or offer for sale, orig. illicitly.
with examples from 1919; but it doesn't give a reason for that meaning.
Without much evidence, I suggest that to flog = to whip = to urge along (as in the "dead horse" analogy). And thus the man flogging the iffy goods, was urging along the sale of the iffy goods: he was encouraging the sale of his own items.