Is it possible to have a positive net income and a negative cash flow from operations?

Yes it is possible.

Here's an example: Near the end of the year you signed a big client. To meet their needs, you have to rapidly increase production. You buy a new production machine with cash, you increase your raw materials inventory, paid for in cash. And just before the end of the year, you ship out your first large order to this new client on 30 day terms, increasing your profits...and receivables (not cash).

Second example, you take advantage of falling interest rates to restructure your debt, paying off a large portion with excess cash.

The OP's examples are wrong: The purchase of production machine would impact cash flow from investing and the "restructuring of debt" would impact cash flow from financing.

Suppose a very "simple" company had an I/S that read:

Revenues: $2

Expenses: $1

Net Income: $1

Now suppose that those revenues were composed of sales made entirely on account. That is, the firm received $0 cash, but their accounts receivable increased by $2. Also, suppose that their only expense was cost of goods sold. This means over the course of the year the firm's inventory account decreased by $1. Lastly, suppose that during the year the firm paid off $4 of its Accounts Payable. We would calculate CFFO like this:

Net Income + Decreases in Current Assets/Increases in Current Liabilities - Increases in Current Liabilities/Decreases in Current Assets

So we would take our net income $1 add back the $1 (inventory) and subtract out the $2 increase in A/R and the $4 decrease in A/P, resulting in $(4). This $(4) is our CFFO.

The rationale behind this process is that our net income was decreased by the COGS, but in reality there was no cash spent so we have to add back the $1. Similarly, our net income was increased by the Revenues, but these were the result of receivables so we have to subtract out the $2 because we didnt receive the cash. Finally, we paid $4 of accounts payable off. This account did not touch the I/S therefore we have to subtract out $4 to reflect the actual cash flow.

Cash flows can be pretty confusing, but as you can see from above it is possible to have positive net income, but negative cash flow. That is why it is important to rely on all the financial statements when making decisions or analyzing companies. If we only rely on the I/S for our decision-making, we will make bad decisions.