Radical-scavenging antioxidants play crucial roles in the protection of unsaturated oils against autoxidation and, especially, edible oils rich in omega-3 because of their high sensitivity to oxygen. Two complementary tools are employed to select, among a large set of natural and synthetic phenols, the most promising antioxidants. On the one hand, density functional theory (DFT) calculations provide bond dissociation enthalpies (BDEs) of 70 natural (i.e., tocopherols, hydroxybenzoic and cinnamic acids, flavonoids, stilbenes, lignans, and coumarins) and synthetic (i.e., 2,6-di-tert-butyl-4-methylphenol (BHT), 3-tert-butyl-4-hydroxyanisol (BHA), and tert-butylhydroquinone (TBHQ)) phenols. These BDEs are discussed on the basis of structure–activity relationships with regard to their potential antioxidant activities. On the other hand, the kinetic rate constants and number of hydrogen atoms released per phenol molecule are measured by monitoring the reaction of phenols with 2,2-diphenyl-1-picrylhydrazyl (DPPH•) radical. The comparison of the results obtained with these two complementary methods allows highlighting the most promising antioxidants. Finally, the antioxidant effectiveness of the best candidates is assessed by following the absorption of oxygen by methyl esters of linseed oil containing 0.5 mmol L−1 of antioxidant and warmed at 90 °C under oxygen atmosphere. Under these conditions, some natural phenols namely epigallocatechin gallate, myricetin, rosmarinic and carnosic acids were found to be more effective antioxidants than α-tocopherol.