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Right, every _share_ purchased is also a share sold (in principle), but that price will not usually be the same price that the current seller originally purchased the share at themselves. As a result, you can have inflow/outflows in dollar amounts. For individuals stocks, with increasing/decreasing market caps, but of course there can be more money in the market overall.

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You misunderstand. Money doesn't flow into or out of markets on net. Every time a share is sold for $X, a share is bought for $X - they are two sides of the same transaction.

This misses that the share is an asset _with a monetary value_ even though it's not money itself. It's true but not relevant that various measures of the money supply, M0, M1, etc. are unchanged.

The chart in the original article is of Annual Equity Fund flows, which are net values _considering both sides since it includes negative values_ -- a measurement of this supposedly nonexistant flow. While money remains constant from a trade, the stock of equity (in both senses of the term "stock") changes.

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