I’d suggest taking the Slayer class to make this character, as you can pick up Ranger Combat styles with Slayer Talents, helping with the feat requirements, and the BAB is higher (so the feat is acquired sooner). You can always multiclass into rogue after level 6.
For myself, I am tempted to build a Nature Fang Druid around this concept...
Anyway, using your first attack to perform a combat maneuver, such as with Quick Dirty Trick (though it has requirements of its own), can set you up for the extra attacks nicely. Looks like you could easily get all of these on 6th level Slayer (including weapon finesse) with a human.
If you go rogue, have a few extra tools. Stealth and flanking come for free, so use them. Mobility makes flanking easier (position yourself at full speed), while Spring Attack works well with the level 8 scout ability (both require you to move 10+ feet). So the prerequisite feats of Circling Mongoose are not just a feat tax.
For a pure rogue, Circling Mongoose can be picked up at level 8, via the combat trick rogue talent. Taking 3 levels of one (or multiple) full BAB classes improves that to level 7 - maybe barbarian 1 + fighter 1 + slayer 1? This would also save you the rogue talent, but delay your access to advanced talents (hmm). The loss on sneak attack can be (mostly) compensated by the Accomplished Sneak Attacker feat.
Two-Weapon Fighting is a good boost at low level - just be aware you will use it only half the time. It works well with knife master, but not with scout which encourages moving around (unless you have pounce from somewhere). Either way, it's good enough to be added to the toolbox.
To get more out of Circling Mongoose, take Outflank. Since you flank with yourself, the feat works more reliably for you. And you need the +2 attack bonus.
Finally, there is the Dirty Fighter combat trait for +1 damage on flanking. It doesn't win battles for you, but it scales with getting more attacks.