The average monthly flow out of unemployment pool of $7.0$ million people each month is $3.1$ million. Put another way, the proportion of unemployed leaving unemployment equals $\frac{3.1}{7.0}$ or about $44 \%$ each month. Put yet another way, the average duration of unemployment - the average length of time people spend unemployed - is between $2$ and $3$ months.
Now, I can't understand how the duration of unemployment is derived and claimed to be $2-3$ months.
On
This sounds like newspaper statistics to me, so I think it is much simpler. If everybody stayed unemployed the same amount of time, it would be $\frac {7.0}{3.1}\approx 2.26$ months. The author then thinks, "We know there is variation, so let's expand that to $2$ to $3$ months." From the data given, we could have $3.9$ million who are permanently out of work and $3.1$ million who are unemployed for a month, or many other combinations. It is certainly not mathematically defensible, but that is not the hurdle in this application.
I also have a hard time figuring out how exactly does one get to this claim of a 2-3 month interval.
On way to obtain a result which would more or less match this 2-3 month contention would be to assume that the process of leaving unemployment is a Poisson process (see http://www.rle.mit.edu/rgallager/documents/6.262vdbw2.pdf).
Then you would have that the time before one gets out of unemployement is a random variable $X$ following an exponential distribution $f_X(x) = \lambda \exp(-\lambda x)$, where $\lambda = 0.44$, the rate at which people get out of unemployment. Under the assumption of a Poisson process, given $X\sim \lambda \exp(-\lambda x)$, you have $\mathbb{E}(X) = \frac{1}{0.44} = 2.27$, which roughly matches the interval of 2-3 month.
Now I realize that this is really farfetched and requires a lot of additional assumption which are not provided in the statement of your question. But it is the best I can think of to make sense of it...