Final answer:
To encourage blood flow from a capillary puncture site, milking the site using gentle pressure is the accepted method. Vigorous massage and cold compresses are not recommended.
Step-by-step explanation:
When performing a capillary puncture and having difficulty collecting an adequate blood sample, the accepted method to encourage blood flow from the site is to milk the site using gentle pressure (Option B). Vigorously massaging the site or using a cold compress can potentially damage the tissue or affect the test results. It is also advisable to keep the puncture site covered after the procedure to prevent contamination or infection.