Advance Auto Parts' cash flow increasing can definitely increase the safety of its dividend yield. This is because cash flow is a crucial factor in determining a company's ability to pay dividends consistently and sustainably over the long term. If a company's cash flow is strong, it can afford to pay dividends even during times of economic uncertainty or a temporary downturn in business.

When a company has a high cash flow, it means that it is generating more cash than it is spending on operating expenses and capital expenditures. This excess cash can be used to pay dividends to shareholders, among other things. However, if a company's cash flow is low, it may struggle to maintain its dividend payments, as it may need to use its cash reserves to cover other expenses.

In the case of Advance Auto Parts, if the company's cash flow increases, it could provide a greater margin of safety for its dividend yield. This is because it would be less likely to experience cash flow issues that could put the dividend in jeopardy. Additionally, a strong cash flow could allow the company to increase its dividend payments over time, which is typically viewed as a positive signal by investors.

It's worth noting that other factors can also impact the safety of a company's dividend yield, such as its level of debt, profitability, and overall financial health. Investors should always conduct thorough research and analysis before making any investment decisions, including evaluating a company's cash flow and other key financial metrics.