In GDP growth studies, are factors of production measured as stock or flows? Consider the following cases:


One machine (capital) is used by multiple producers within one year. For instance, farmers renting tractors from the same company. In this case, in terms of GDP, there is one unit of capital which was used to produce value added by many producers.
One worker (labour) which have two jobs. For instance, in a factory during the day, and as a Uber driver during the night. In this case, in terms of GDP, there is one unit of labour, used to produce value added in different goods/services.


The common feature is that the same factor of production (stock) is employed in more than one activity over a given period (flow).

Is the measurement of capital and labour used in the standard "determinants of growth" studies based on the stock or flow approach?

In other words, are capital and labour measured in terms of the flow of services that these factors produce, or in terms of the stock of factors available in an economy over time? It is clear to me that the latter approach is plagued with problems, and the former is clearly more accurate.

My experience is that the use of stock is more common.
In Nicholas Stern (1991)'s The Determinants of Growth first equation (I a), without preconceived ideas, one reads

$\frac{\dot{K}}{K} 
= \frac{d K}{d t} \frac{1}{K}$

Which means explicitly (in discret values)

$= \frac{K_{t+dt}-K_{t}}{dt} \frac{1}{K_{t}}$

If $t$ is in years, and that we are interested in the variation of $K$ over $1$ year (i.e. $dt=1$), one obtains

$= -1 +\frac{K_{t+1}}{K_{t}}$

Even if the above equality could represent either the variation of a stock or the variation of a flow, the story behind this is about stocks. To summarize


$K_{t}$ is the stock of capital in the economy at year $t$
$dK = K_{t+dt}-K_{t}$ is a flow of capital occuring at year $t$, differently put an investment in capital.
$\dot{K}=\frac{d K}{d t}$ is the absolute dynamic of investments in capital in economy $\forall t$
$\frac{\dot{K}}{K}$ is the relative dynamic of investments in capital in economy $\forall t$


Depending on the object you are looking at, it can be both measured in flow or in stock. To know with what you are dealing with, you must understand the story behind equations.

To the practice side of the issue, you cannot make realistic analogy between Solow's capital and, say, tractors. The least abusive perception of $K$ would be cumulated flows of investment in terms of money since, for example in micro-based CGE modelling, it is conceived as representative of the shareholding structure of the economy, and is thus linked to income formation via dividends (see the zero profit condition). In this non-realistic framework, although non-abusively linked to the everyday-life object, $L$ is very similar to $K$, is a self owned stock, and gives right to wages, that are flow objects, as dividends are. Still on the practice side of the issue, the difference between $L$ and labor force is the fact that the former is effectively employed, while the latter is not. Put differently, the link between the two is the labor market, $L$ is a demand, while labor force is a supply, and both form jointly a labor market whose equilibrium is reached via deflation/inflation of wages.

Finally, to my knowledge, the fact that  the same factor of production (stock) is employed in more than one activity over a given period (flow). is not really a neoclassic native notion, I would say, once again when one refers to CGE modelling, because of the capital market clearing condition. It is more a monetary-macro-financial object, and is, e.g. all what debt is about when dealing with capital. However I do not see any analogy with $L$ in this case.