Medieval and Renaissance flags and banners to study from extant examples in museums, as well as links to articles discussing extant flags and banners. Not so much about banners as depicted in period artwork; other webpages, like these links on heraldic banners and flags, do a good survey of that sort of thing.

See The Sable Rose - Banners and Flags for information on late 15th century European banners, and how they were made. Cennini's Libro dell'Arte – especially this section – is useful for understanding craftsmen's techniques and materials.

• Armory as Self-Representation includes a photo of the 14th century banner with the arms of the dukes of Savoy with the family arms of de Blonays, in a combination of appliqué and embroidery (another photo here).
• The Banderia Prutenorum of Jan Długosz (Teutonic Knights' gonfalons collected after the Battle of Grunwald), 1410
• Banner with three crowns, mid-15th century
• Banner for the city of Ghent, painted by Agnes van den Bossche ca. 1482 (also here)
• Bandiere di Borgogna includes illustrations and some extant examples from the Burgundian Wars, c. 1474-1476
• Banner with double-headed eagle, ca. 1500
• The Dacre Ram, Gryphon, Bull, and Dolphin, c. 1507-1525 (they're holding 19th century banners)
• Ceremonial standard, associated with the Douglas of Cavers Family, probably from the late 16th century
• Funeral banner of Oliver Cromwell, 1658
• The Sable Rose Grimoire: Banners and Flags describes extant banners in general, including materials and construction.

Including church banners and processional banners. (I’m setting these apart from the flags and banners in the section above, but they do still show the sorts of techniques and materials that might have been used for heraldic banners.)

• 14th century Byzantine banners at the Halberstadt Dommuseum: 87 781, 87 783, & 1.083 448
• The Crucifixion with the Virgin and Saint John; St Anthony Abbot at the foot of the Cross, a double-sided processional banner (painted in tempera and gilt on canvas) attributed to Barnaba da Modena, c. 1370
• The Madonna of Humility by Lippo di Dalmasio, c. 1390-1400; The Grove Encyclopedia of Materials & Techniques in Art suggests that this “is probably the remnant of a processional banner such as [Cennini] described.”
• Processional banner of the Confraternity of Saint Mary Magdalene in Borgo San Sepolcro, painted by Spinello Aretino, c. 1395–1400
• Italian or Spanish processional banner, 15th century
• Procession banner: The Virgin and Child with St. Lazarus, c. 1502 (also here)
• A few 16th century flags in various media relating to St. Sebastian (St. Sebastian's guild): c. 1501-1700, c. 1501-1600, c. 1501-1700, 1527, 1564
• Runner square of the banner of Julius II, 1513
• Photos of the Fetternear Banner, embroidered around 1520 and the only known Scottish church banner from that period, can be found using the search engine at National Museums Scotland
• Greek processional banner, 16th century
• Embroidered banners from Kerk Sint-Jacob, c. 1541-1560: the Descent of the Holy Spirit and Christ risen from the grave, c. 1541-1560