So on the military side of things, I’ve yet to find any evidence to a link to Stanley McChrystal, but I’ve found plenty of evidence of military service in the wider McChrystal family.
Michael Thomas Aloysius McChrystal (elder brother of the Arthur McChrystal who left for America) served as a Driver (read: Horseman) in the Royal Field Artillery during WWI. He served with 4 Battery VII Brigade RFA. They were stationed as part of the 2nd Rawalpindi Division in what was then India (now Pakistan) for the duration of the war. He was probably mostly stationed in Abbottabad - more recently famous for being the site of Bin Laden’s death. Michael also likely fought in the Third Anglo-Afghan war, a brief cross-border conflict in 1919 that saw Afghanistan gain full political independence from Britain.
James Redmond McChrystal, another of Arthur’s brothers, served with the 7th Battalion Loyal North Lancashire Regiment (a battalion also known as the Preston Pals). He served in France for the duration of WWI.
Another possible brother of the Wigan-based McChrystals was John McChrystal who served with the King’s Own Royal Lancasters. This man received two bravery awards, the Distinguished Conduct Medal (DCM) and the Military Medal. I’ve yet to confirm that this man is indeed linked. Probably need to try and find his marriage record to check his father’s name is Arthur to fully confirm.
Finally, I’ve found another Michael McChrystal (cousin of my great-grandmother, son of my 2x great grandfather’s brother John). He was working as a messenger for the General Post Office in London EC1 before the war. He then seems to have served as a Kite Balloon spotted looking for submarines off the South Coast of England at Berry Head!