I have questioned the date that Blackburne gave - See "Flaws (Part I)" - as the August 15, 1885 issue of the Brooklyn Chess Chronicle (J.B. and E.M. Munoz, editors) presented the game as having been "played some months ago" which would suggest that it was played during 1885, but not likely in July or August of that year.
It now looks like I will have to back off from my correction, and add even more uncertainty to the date of the game.
Tim Harding's Joseph Henry Blackburne A Chess Biography (2015) - which, as I have noted, does not give Amateur - Blackburne - shows that the British master left for Australia in December 1884, and spent the first half of 1885 "Down Under". A return home was short-lived, as there was an important tournament to participate in
Blackburne and son apparently disembarked at Plymouth on 4 July. As the ship was only docked at Gravesend on the fifth, they must have come up to London by express train. Every day counted, the first round in Hamsburg being on 12 July. After less than a week in England, Blackburne was off on his travels again.
The Hamburg tournament ended July 27, wherupon Blackburne went to Hereford for the Counties Chess Association Masters tournament, which started August 3.The events of 1885, therefore, do not appear consistent with the Brooklyn Chess Chronicle admittedly casual dating.
It is possible to extend Munoz and Munoz's "some months" further back in time and look for Amateur - Blackburne in 1884, although there are difficulties in this, too. Harding notes
Blackburne's mid-career health breakdown began before Christmas 1883 when he was forced to cancel all his engagements.In an age "long before antibiotics or even aspirin and other effective medicines", Blackburne was quite ill.
In late April or early May  he resumed playing at the [Simpson's] Divan; some casual games are preserved from that period...However, his participation in Simpson's handicap tournament in the spring was affected by his "unfortunate illness" and it is worth noting
[T]he Morning Post, 30 June 1884, said that Blackburne's illness had "left him in a weak state of health, and has prevented him for several months from pursuing his avocation."Although he travelled to Glasgow the last week in July 1884, it does not appear that his full health returned before his trip to Australia.
Unless I guess "late April or early May" 1884 (above), then "about 1880" (from Blackburne's book) will be as "precise" as I will be able to date Amateur - Blackburne, until another chess column, magazine, or book reference surfaces; especially if we recall the uncertainties mentioned by Brazilian chess master Hindemburg Melão, Jr. in his article for the online chess site, SuperAjedrez,
...Some sources indicate year of the game as 1868, others indicate 1888, and others indicate 1880. Some sources affirm that it was played in Manchester, others in London. Normally the name of the adversary is not given, having only "NN" or "Amateur", but in at least one source "Millner" is indicated as the name. Also it is not known if it was an individual game or part of a simultaneous display... [T]he game deserves to be cited as one of most beautiful pearls of blindfold Chess...