Zimbabwean all-rounder Elton Chigumbura is the club's overseas signing, and Loye returns to his hometown club after seven seasons at Lancashire.
Flintoff had Kyle Coetzer fending a short ball to Loye in the slips, bowled Ben Harmison, had Steve caught behind and bowled Claydon.
After Lancashire won the toss, openers Paul Horton (37) and Mal Loye (18) shared 47 before Loye fell lbw to Lancashire old boy Cork.
Loye and Vincent shared 112 to guide Lancashire to a 10-wicket win over Derbyshire earlier this month and were close to a similar feat.
Lancashire lost Lou Vincent cheaply but opener Mal Loye hit five fours and a six before he top-edged a reverse sweep to point for 32.
Middlesex started the final day on the front foot when seamer Tim Murtagh found Mal Loye's edge, earning a catch for England captain Andrew Strauss.
After removing top-scorer Mal Loye (39), Flintoff, Luke Sutton and Kyle Hogg, Davies then dismissed skipper Stuart Law to make it five in 17 balls.
Snell benefited from being dropped at gully by Mal Loye to complete a 58-ball half-century before Brooks trapped him leg before to seal a comprehensive win.
And, when Northants went in again, it was the same story, as Peters, Loye and Vishal Tripathi were all out for the second time in the day.
Chilton and Mal Loye both fell to the off-spin of Paul Wiseman (4-87) before Horton and Yousuf put on 74 for the third wicket as the lead steadily grew.
Loye hit a six in the first over of the Lancashire reply and added another with a slog sweep off Graham Wagg, before Vincent recorded his first 20-over hundred.
Hoffmann gave Scotland hope when he trapped trapped Mal Loye lbw for 15 before Mark Chilton got a leading edge off Dewald Nel to spoon a catch to Hamilton.
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Loye was particularly creative as he collected eight fours and a leg-side six, before Law and Kyle Hogg, who blasted 24 off just 14 balls, provided impetus towards the end.
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And, after James Franklin made the first breakthrough, Hussain marked only his second Championship appearance with a spell of 3-8 from five overs, removing Mal Loye, David Sales and Stephen Peters.
An experimental Lancashire side, missing the likes of captain Glen Chapple, Mal Loye, VVS Laxman and Francois du Plessis, were skittled for just 166 in the 40th over after they batted first.
Doshi's Surrey team-mates Ali Brown and James Benning are others whose names have been put forward because of their uninhibited strokeplay, along with Lancashire's Mal Loye, who was part of England's one-day squad in Australia last winter.
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