Given, discharge data alone for each month in each year, is it possible to calculate the flow duration curve? Some of the discharge values in some months were found to be 0. Do we need to consider those values?
Spreadsheets work well for this.
You have 12×12 observations so use 144+1 = 145 as the number of observations for calculating your probabilities.
Put your discharge data in a column and sort from highest to lowest. Put a column of Rankings next to it and number from 1 up to your maximum (1 to 144). Put a column next to that and calculate your probability of exceeding each discharge value:
P = Ranking×100/145
(P as a percent)
Graph discharge vs. P.
You need to consider your 0 discharge months in determining the number of periods but you don't need to calculate P for them. That's handy if you don't want errors in plotting log discharge vs. P.