Everything about this person is highly uncertain. The general idea is that his supposed grandson also named Amaury is a relative of the Reginar family of Hainaut.
According to the History of the Bishops of Cambrai, written about 1041, Amaury, a count from the region (pagus) of Hainaut (not count of Hainaut, as sometimes stated), who was married to a daughter of Isaac, count of Cambrai, was related to his wife within a prohibited degree, and was therefore divorced from his wife by Fulbert, bishop of Cambrai (934-956), possibly about 950 ["Alter itidem comes ex pago Hainou, Amulricus nomine, vir genere nobilissimus et iuxta secularis gloriae pompam fortunatissimus, filiam Isaac aeque comitis prefati duxit uxorem. Multis autem internoscentibus atque deferentibus conperiens Fulbertus episcopus, eos, sponsum videlicet et sponsam, proximae cognitionis consanguinitate propinquos et ideo contra legem copulatos, facto consilio canonice ab invicem seiunxit, datoque poenitentiae modo, hoc tantum scelus admissum expiari precepit." Gesta Episcoporum Cameracensium, i, 74, MGH SS 7: 427; the notice appears in the history immediately after an act of Otto I dated 30 April 947, and immediately before an account of the Hungarian invasion in 953]. Amaury (Amelricus) appears with a count Richizo in an act of the emperor Otto I dated 12 February 973 ["... fidelissimorum nostrorum Richizonis atque Amelrici comitum interventu ..." MGH DD O I 579 (#426)]. Duvivier suggested that Amaury was count in the eastern part of the pagus of Hainaut [Duvivier (1865), 91]. Vanderkindere offers the theory that Amaury was count of Valenciennes [Vanderkindere (1902), 71-3, 88 (table)]. Neither mentioned a possible connection of count Amaury with Guillaume de Hainaut or Amaury de Montfort.
The suggestion that Amaury was the father of Guillaume de Hainaut has no strong basis, but is a conjecture based partly on the supposed connection of both Amaury and Guillaume with Hainaut and partly on the name Amaury. The conjecture is plausible enough, but falls far short of proof.
Concerning the line further back, MEDLANDS does give apparently one source which would make this Amaury (or someone in his position in the family tree) the son of Reinier II. Under Amaury's supposed son Guillaume of Hainaut, he Cawley writes:
Dion suggests that he was a cousin of Reginar [IV] Comte de Hainaut
The citation is to Dion ‘Le Château de Montfort’, Tome I (1873), p. 122.
It may be possible to confirm family relationships with Amaury by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
Y-chromosome DNA test-takers in his direct paternal line on WikiTree: