Quin has a Cockney Accent developed from living in England for well over a century. A good reference point would be Sniper from TF2. If you dont know who that is, YouTube 'Meet the Sniper' and you'll get the idea.

Other characters to try and emulate:

Captain John Price, Call of Duty: Modern Warfare series

Sergeant Wallcroft, Call of Duty: Modern Warfare Series

Simon 'Ghost' Riley, Callof Duty: Modern Warfare 2

(Why 3 from Call of Duty games? British, military men, SAS, they sort of also encompass part of his archetype)

Who NOT to emulate:

Overboss Colter, Fallout 4: Nukaworld

(If your attempted reminds you of a goon from a movie, please try again. If we listen to it and it gives us an evil impression, needless to say this part won't be having you but there are plenty of evil sounding British guy parts.)

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Quin's ethnically an ancient Greek,  a Hero*, and a trained hoplite. 

Born the son of Hades and Persephone as a Halfing Hero with no legitimate powers beyond being biologically immortal, durable, and reflexive. An event that still needs fine tuning left him with some blood on his hands that has rendered him a psychosis ridden mess. The situation in question has guidelines as follows; he needed to kill the person he wanted to save, Erica is involved in a 'positive way', psychosis follows. Immediately after this event he became distant and aggressive, unable to get close to anyone and unable to move on from the event as a result. He traveled around for a time (resulting in his British Nationality and eventual vigilantism in America). 

He's a hard nut to crack, comparable to the tsundere (ie, impossible to get to know until enough time and effort is made). He's experienced beyond most other characters. Where Flak is confident out of personality, Quin is a one man army out of pure skill. Due to several bad encounters as well as his annoying 'friend' Flak Zoleni, Quin holds a certain distrust of magic.