Base Monk gives two feats at first level, not including Improved Unarmed Strike. Second level nets you another bonus feat, for 2 at 1st level, and 1 more at 2nd, + IUS. Monk of the Sacred Mountain and Zen Archer Monk both give you two feats on first and second level (Stunning Fist, Toughness, Bonus Feat 2x, or Perfect Strike, Weapon Focus, Bonus Feat 2x), in addition to proficiencies and Improved Unarmed Strike. Zen Archer also gives a single feat at 3rd level (Point-Blank Master). Qinggong Monk can pseudo-acquire a single feat at 4th and 5th levels, and can combine with Zen Archer, which gets two feats at 6th level (Weapon Specialization and Bonus Feat). If you count the pseudo-feat acquisitions, you could have 9 feats over 6 levels, or 4 feats over 2 levels if you don't count that. In comparison, Far Strike Monk gives you two feats at 1st level + Improved Unarmed Strike, 3 by 2nd, or 4 at 4th.
Just for the purpose of this, we're not going to count the Unarmed Fighter or Unchained Monk's variety of exotic Monk weapon proficiencies as separate feats.
Monk: (2 feats+IUS over 1 level, 4 feats+IUS over 2 levels, or 9 feats+IUS over 6 levels) - requires Lawful
UMonk: (?+1 feat+IUS over 1 level) - requires Lawful
Bloodrager isn't a good source of feats. The best you can do is with Bloody-Knuckled Rowdy, for Improved Unarmed Strike at 1st, and maybe a combat style feat at 2nd, in addition to your martial weapons, shields, and medium armor. Alternatively, Steelblooded gives you heavy armor at 1st.
Bloodrager: (1 feat+IUS over 2 levels, or just IUS for 1 level)
Swashbuckler gets you a specific alteration of Weapon Finesse, as well as Panache. If you don't count Panache as a set of feats (you can get Panache through feats), then you get 1 feat. However, Inspired Blade Swashbuckler nets you a free Weapon Focus, at the cost of narrowing your Weapon Finesse applicability. Mysterious Avenger and Roldelero get exotic weapon proficiencies, but that's basically out of bounds.
Swashbuckler: (1 feat over 1 level+WF)
If you take a careful look at the Deific/Celestial/Demonic Obedience feats, you might notice that some of them are basically multiple feats. The Celestial Obedience feat for Olheon (who even is this guy?) gets you free Leadership at 20th level. The Deific Obedience (Evangelist, or default one) nets you Extra Revelation at 20th, if you are an Oracle. The Deific Obedience for Asmodeus (Evangelist, or default) snags you Favored Judgement at 16th. And the Deific Obedience for Zuursvaater (Sentinel, so requires Sentinel PRC) nets you proficiency and Weapon Focus in everything (or rather lets you treat everything as if you were proficient and had Weapon Focus in it). Sentinel itself grants 2 feats over 9 levels, which is a poor trade. But if you're counting proficiency and (effective) weapon focus in every weapon as feats, then it's definitely worth it.
Celestial Obedience: (2 feats for 1 feat) - Requires LG
Deific Obedience: (2 feats for 1 feat) - Requires TN or LE
Sentinel: (?+2 feats over 9 levels) - Requires LE, Deific Obedience feat
Also, Animal Companions can be acquired through feats, so if you use the dubious logic of "if I can get this through feats, it counts as feats", then an Animal Companion would have Nature Soul and Animal Ally. Similarly, Familiars would count as three feats via Iron Will, Familiar Bond, and Improved Familiar Bond. Thus any Sorcerer or Wizard with a Familiar would count as having 3 feats from that alone, in addition to the Alertness granted. Otherwise, you have 2 feats - Alertness and either Scribe Scroll, Eschew Materials, Sahir-Afiyun, or Varisian Tattoo. You can't take both, though.
Sorcerer: (5 feats over 1 level, or 2 feats over 1 level)
Wizard: (5 feats over 1 level, or 2 feats over 1 level)
Speaking of Sorcerer, the most efficient way to use Sorcerer features to get more feats is through Eldritch Heritage. Improved Eldritch Heritage (Impossible) picks up Craft Wondrous Item, with a little extra bonus to craft without having the spell.
Eldritch Heritage: (4 feats for 3 feats)
