I am having a little confusion on the best way to play flopped sets. Here is one recently

PokerStars Pot-Limit Omaha/8, $0.02 BB (8 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

UTG+1 ($2.64)
MP1 ($1.26)
MP2 ($1.56)
CO ($1.80)
Button ($1.61)
Hero ($0.98)
BB ($4.28)
UTG ($4.47)

Preflop: Hero is SB with T, T, A, 3.
UTG calls $0.02, UTG+1 calls $0.02, MP1 calls $0.02, 1 fold, CO calls $0.02, 1 fold, Hero completes, BB checks.

Flop: ($0.12) 6, T, K (6 players)
Hero checks, BB bets $0.04, UTG folds, UTG+1 folds, MP1 calls $0.04, CO calls $0.04, Hero raises to $0.32, BB calls $0.28, MP1 folds, CO folds.

Turn: ($0.84) 2 (2 players)
Hero checks, BB bets $0.2, Hero calls $0.20.

River: ($1.24) 6 (2 players)
Hero bets $0.44 (All-In), BB calls $0.44.

Final Pot: $2.12

im not sure what youre confused about. the only thing i see is that given your stack size and the way you played the flop (which i love btw) i think you have to shove the turn almost without looking at it.

if you lost this hand to kings oh well. you werent deep enough to find a fold unless you just check/folded the flop (which would be bad, this isnt middle set on a 269 board this middle set has some value to it).

You played this perfectly on all streets.
Villain is an idiot (whatever he had) and you should add him to your friends list.