The relevant Wikipedia page has a large gap between 1961 and 1984, not allowing to estimate, even approximately, in what year the symbolic threshold of $1/FLOPS (or, as the wiki table puts it, $1bn/GFLOPS) was crossed.
The threshold of $1/KFLOPS is interesting as well.
In this case the Soviet data points would be mostly useless because the prices of goods not sold outside of the Eastern bloc were in funny money.
If we attempt to accept funny money at a face value, a potential contender – BESM-6 (1967) – still doesn't do it.
A figure of just below $1M was alluded to (in Russian; computed as a multiple of a publicly quoted price of 600K rubles, and the official exchange rate of $1.56 per ruble; I also remember it reported regularly in Soviet newspapers as 0.64-0.66 rubles per dollar), but delivered at most 0.5 MFLOPS using the most generous definition.