my top 'office carries' (smaller, lighterweight blades, ok to pull out around almost anyone) all come up short in some category of what you're looking for:
-buck vantage pro small - deep pocket carry, flipper (flipper is not that good on the small compared to the large), s30v steel. it's a LOT smaller than the large if that's what you've alreay got. might be worth a look if you have and like the large, b/c it's quite a bit smaller.
-benchmade mini-griptilian - love mine, not a flipper open (i've got the one with the spydie hole). everything else fits, except not a super deep carry.
--i had but got rid of the benchmade mini-barrage - not a flipper, but assisted open. good one, fun AO, just didn't make the rotation enough. also not a deep carry clip
-spyderco chaparral - thin, nice lines, lightweight, s30v steel. not a flipper, and it's a linerlock. love this one, but comes up short in 2 diff categories for your want. great deep carry clip, though
-sebenza insingo & sebenza classic smalls - blows the budget, not a flipper, but awesome knives. i prefer the lines of the insingo myself, both are great. not super deep carry, but made really really really well.
if you like the sebenza's overall look but they're too much scratch - bradley alias???
to second the ken onion ripple- i really liked the initial look, liked the flipper action, just didn't fit my hand at all. kind of odd, but made it a pass for me. nice knife, though.
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also, STR has a forum under 'Makers' here on BF. and he can make a deep carry clip for a LOT of knives. if you find one that fits all the other categories, check with him re: making you a deep carry clip. i think about $30ish usually. good luck in your hunt!