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Working Capital Definition 
As you say, if you delay paying your bills, your liabilities will increase. Like say your bills total $10,000 per month. If you normally pay after 30 days, then your short-term liabilities will be $10,000. If you stretch that out to pay after 60 days, then you will be carrying two months worth of bills as a short-term liability, or $20,000. Your liabilities go up. Assume you keep the same amount of cash on hand after you stretch out your payments like this as you did before. Now your liabilities are higher but your assets are the same, so your working capital goes down. For example, suppose you kept $25,000 in the bank before this change and you still keep $30,000 after. Then before your working capital was $25,000 minus $10,000, or $15,000. After it is $25,000 minus $20,000, or only $5,000. So how does this relate to cash flow? While presumably if the company has $10,000 per month in bills, and their bank balance remains at $25,000 month after month, then they must have $10,000 per month in income that's going to pay those bills, or the bank balance would be going down. So now if they DON'T pay that $10,000 in bills this month, but the bank account doesn't go up by $10,000, then they must have spent the $10,000 on something else. That is, they have converted that money from an on-going balance into cash flow. Note that this is a one-time trick. If you stretch out your payment time from 30 days to 60 days, then you are now carrying 2 months worth of bills on your books instead of 1. So the first month that you do this -- if you did it all at once for all your bills -- you would just not pay any bills that month. But then you would have to resume paying the bills the next month. It's not like you're adding $10,000 to your cash flow every month. You're adding $10,000 to your cash flow the month that you make the change. Then you return to equilibrium. To increase your cash flow every month this way, you would have to continually increase the time it takes you to pay your bills: 30 days this month, 45 days the next, 60 the next, then 75, 90, etc. Pretty soon your bills are 20 years past due and no one wants to do business with you any more. Normally people see an action like this as an emergency measure to get over a short-term cash crunch. Adopting it as a long-term policy seems very short-sighted to me, creating a long-term relationship problem with your suppliers in exchange for a one-shot gain. But then, I'm not a big corporate finance officer.