The 1918 "Spanish Flu" pandemic (the speculation about the actual source of the virus is adequately covered in the Wikipedia article) occurred in three waves.
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The first wave in Europe and the US peaked in early 1918 while the First World War was being fought (and the German Spring Offensive was being fought on the Western Front. The second (and more deadly) wave peaked in the autumn (northern hemisphere) of 1918, as the war was ending, while the third and final wave peaked in early 1919.
As observed in comments, the economic impacts of the flu pandemic can be difficult to separate from the much larger impacts of the First World War itself. As observed in the article The Spanish Flu and the Stock Market: The Pandemic of 1919
Of course, the Spanish flu occurred in 1918 while World War I was raging in Europe so the war had a larger impact on the stock market than the flu. There were few if any global supply chains that the Spanish Flu could disrupt because the war made supply chains nonexistent.
The article August 1914: When Global Stock Markets Closed includes some helpful graphs which show how the Dow Jones Industrial Average performed immediately prior to the First World War breaking out in Europe, and how it performed over the duration of the war as a whole. That article also discusses how some European markets were restricted during the war, which is why we might not expect to see any direct impact from the pandemic there.
What is, perhaps, remarkable is that markets did not seem to show any significant positive reaction to the end of hostilities in November 1918. In the article The Spanish Flu and the Stock Market: The Pandemic of 1919, cited above, Dr. Bryan Taylor makes the same observation and suggests that any "bounce" due to the end of the war had been offset by concerns about the flu:
It is interesting that there was little impact on the stock market of World War I ending on November 11, 1918. Perhaps euphoria about the conclusion of the war was offset by concerns about the Spanish flu.
They go on to observe that after the third and final peak had passed in February/March 1919:
... the market began an increase of 50% which lasted until November of 1919. Whether this increase occurred because of the end of World War I or the end of the flu or both is impossible to say ...
This rise began before the Treaty of Versailles was signed, and so presumably cannot be linked directly to that event. Nevertheless, rumours of the progress being made would inevitably have had some (presumably positive) impact on markets.
So it seems likely that the primary observable economic impact of the "Spanish Flu" pandemic may have been to delay the start of the economic recovery from the First World War.
However, that being said, it should be noted that in their 2008 paper Macroeconomic crises since 1870, Robert J. Barro and José F. Ursúa identified macroeconomic effects (defined by declines in per-capita GDP and/or consumption) in the early 1920s (including the 1921 recession) which might be attributable to the pandemic rather than the effects of the First World War. The relevant data is tabulated in their paper should you wish to analyse it further.
Estimates of the number of people killed by the pandemic worldwide vary from about 17 million to almost 100 million (for context, between 20 and 22 million people died in the First World War), with a majority of those killed being young adults.
The uncertainty about the numbers killed arises for two reasons. Firstly, reporting restrictions in the belligerent nations meant that any news which might have a negative impact on morale or which might suggest a weakness to the enemy was censored. This is why the pandemic came to be known as "Spanish Flu". The press in Spain (which was a neutral country) was not subject to the same censorship rules, and so the first cases to be reported were in Spain. Secondly, at the time, influenza wasn't a notifiable disease. As a result, cases of influenza didn't have to be reported, so people simply weren't collating totals of how many had died.
While the impact is impossible to quantify, the loss of so many people from the population of working-age adults would certainly have exacerbated the economic and societal impacts due to those lost while fighting during the war.
Dr Alice Reid makes this point in her paper The Effects of the 1918–1919 Influenza Pandemic on Infant and Child Health in Derbyshire
Although the widespread sickness undoubtedly placed additional strains on society and the economy, these appear to a large extent to have been subsumed into the experience of the war itself.
The combined losses from the war and the pandemic undoubtedly helped shape the Lost Generation, and the post war economic and societal landscape. Whether it is meaningful (or even possible) to attempt to separate relative impacts of those lost to the flu pandemic from those lost while fighting in the war is another question.