You're so close!
Change
plot "print_1012720" using 1:2 title "Flow 1", \
plot "print_1058167" using 1:2 title "Flow 2", \
plot "print_193548" using 1:2 title "Flow 3", \
plot "print_401125" using 1:2 title "Flow 4", \
plot "print_401275" using 1:2 title "Flow 5", \
plot "print_401276" using 1:2 title "Flow 6"
to
plot "print_1012720" using 1:2 title "Flow 1", \
"print_1058167" using 1:2 title "Flow 2", \
"print_193548" using 1:2 title "Flow 3", \
"print_401125" using 1:2 title "Flow 4", \
"print_401275" using 1:2 title "Flow 5", \
"print_401276" using 1:2 title "Flow 6"
The error arises because gnuplot is trying to interpret the word "plot" as the filename to plot, but you haven't assigned any strings to a variable named "plot" (which is good – that would be super confusing).