The chlamys was a short cloak made from a single piece of cloth, with a straight side fastened about the neck, clasped at the shoulder, and having a rounded lower side; cf. Tarbell (284).
[1] For this material cf. (e.g.) John of Antioch fr.33 FHG (now 61.1 Roberto), John Malalas Chronographia II.8 Thurn (24). On Numa see nu 456, nu 515; on the Isaurians, iota 616.
The Suda evidently garbles the historians' account. Traditionally, Numa Pompilius (cf. OCD4 s.v. Pompilius, Numa), the second king of Rome, ruled from 715 to 673 BCE. The Romans would not encounter the Isaurians, a people of the mountainous interior of southern Asia Minor, until after the conquest of Greece (ca. 215-146 BCE), probably in early C1 BCE.
Malalas explains (ibid.) that Numa became acquainted with the chlamys upon his reception of an embassy from the Pelasgians (cf. pi 934), the aboriginal people of the Aegean region; this timeline makes sense. Moreover, Malalas (ca. 491-573 CE) only observes by way of example that his contemporary Isaurians also wear this short cloak; cf. Jeffreys et al. (16).
The ornament on a Roman senator's shoe did not at all resemble the letter 'kappa', but was rather a moon-shaped clasp, the lunula; cf. Staveley (32).
[2] cf. Diogenianus 5.14 and other paroemiographers.
[3] This is Syloson II, tyrant of Samos in the last quarter of the 6th. century BCE; see also sigma 1349 and sigma 1351. For Dareios (I) of Persia, see delta 72, delta 73.