Gnuplot draw two plots on the same graph with single column data

You can't do this without modifying something about the way you input the data. When feeding gnuplot data via standard input, it expects multiple data sets to be delimited with two blank lines between them, or to be interleaved on successive lines. The options are:

• Feed the two data sets into different plot commands altogether.

• Change the file format so that data sets have blank lines between them, then reference them all with index.

• Change the file format so that alternating lines represent different data sets, then reference them all with every.

• Put the data into one file, the plotting script into another, and then reference the data file more than once with different using clauses each time.

There's an intro to the every and index commands starting at How do I plot several data sets in a single file? Those are the only facilities built into gnuplot for this sort of thing, and neither does exactly what you were asking about. it's good you've already modified the data formatting, because this wasn't ever going to work as you'd originally hoped.

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).