Deflate level and flow variables using PPI and CPI What do statements like

Flow variables (such as dividend growth and returns) are deflated using the CPI index.

or

Level variables are deflated using the Producer Price Index (PPI).

mean?

What are level varibales?
I guess both indices correct for inflation but why would dividend growth/returns need to be adjusted?
How does one actually implement this deflation of variables? Is there a time series of the CPI and PPI available only and one simply has to multiply a particular variable with the index?
Level (also called stock) variable, is a variable that measures something at a given point of time. For example, measuring GDP in 2017 would be a level (stock) variable.
Flow  variable is a variable that measures the rate of change in the stock over time. For example, if GDP growth (which measures flow of GDP) was $10\%$ in 2017 that means that the level/stock of GDP increased by $10\%$.
Wikipedia actually has surprisingly excellent explanation on differences between level/stock and flow/growth variables that you can read here (see the general use part).
There is no reason why you would always want to apply CPI to flow variables and PPI to level variables. This must be something that is specific to the research you are reading and there must be some other reason behind it.
If you want to deflate a level variable using some particular deflator you can use the following formula:
$$Real X = \frac{Nominal X}{deflator/100}$$
If you want to adjust flow variable then you can first calculate the change in deflator and subtract that change from the flow variable that is:
$$ g_r  = g_n - \pi$$
where $g$ is the real ($r$)/nominal ($n$) flow/growth rate respectively and $\pi$ inflation rate which is the change in deflator. Also the above is a first order approximation. The exact formula is given by $1-g_r = \frac{1+ g_n}{1+\pi}$ but this exact formula is not often used.