The profile of phenolic compounds changes during the growth of a plant and this change affects its antioxidant potential. The aim of this research has been to find the growth stage of flax with the highest antioxidant capacity, and to determine the phenolic compounds responsible for such a capacity. Flax was harvested in six growth stages: from stem extension to mature seeds. The phenolic compounds were identified using LC–TOF–MS and quantified in an extract and in the fresh matter (FM) of each growth stage. The radical scavenging activity against ABTS•+ and DPPH•, the ferric-reducing antioxidant power (FRAP), and the antioxidant activity in the β-carotene-linoleic acid emulsion system were determined. Mono- and di-C-glycosyl flavones were found to be the most abundant phenolics of the aerial parts of flax, which also showed the highest content of isoorientin (210–538 µg/g FM). Coniferin, its derivative, and hydroxycinnamic acid derivatives were also detected. The plant was richer in flavone C-glycosides from stem extension to seed ripening (1105–1413 µg/g FM) than at the mature seed stage (557 µg/g FM). Most of the individual flavone C-glycoside contents in the extracts decreased when increasingly older plants were considered; however, the isoorientin content did not change significantly from the steam extension to the seed ripening stages. The antiradical activity against ABTS•+ and FRAP was higher for the aerial parts of the flax harvested at the flowering, brown capsule, and seed ripening stages, mainly due to the presence of flavone C-glycosides. The oxidation of β-carotene-linoleic acid emulsion was instead inhibited more effectively by the extracts from plants at the brown capsule and mature seed stages. Coniferin and its derivative were significantly involved in this activity. The extracts from the aerial parts of the flax harvested from flowering to seed ripening could be a valuable source of flavone C-glycosides for use as nutraceuticals and components of functional foods.