Full Tilt Poker $0.02/$0.05 No Limit Hold'em $0.01 Ante - 5 players

Hero (SB): $7.51
BB: $17.22
UTG: $10.00
CO: $11.72
BTN: $5.00

Pre Flop: ($0.12) Hero is SB with J A
Hero raises to $0.20, 3 folds, BTN calls $0.15

Flop: ($0.47) Q 8 7 (2 players)
BTN checks, Hero bets $0.30, BTN calls $0.30

Turn: ($1.07) 5 (2 players)
BTN checks, Hero checks

River: ($1.07) 4 (2 players)
BTN bets $1.07, Hero?

Should I shove this river?

I just sat down and this hand occured 2 hands prior to the above hand:
(Villain in top hand is MP in bottom hand.)

Full Tilt Poker $0.02/$0.05 No Limit Hold'em $0.01 Ante - 6 players

Hero (CO): $7.53
BTN: $17.24
SB: $10.00
BB: $12.06
UTG: $7.24
MP: $5.00

Pre Flop: ($0.13) Hero is CO with 6 Q
UTG raises to $0.10, MP calls $0.10, 4 folds

Flop: ($0.33) K K 6 (2 players)
UTG bets $0.36, MP calls $0.36

Turn: ($1.05) 9 (2 players)
UTG bets $0.26, MP calls $0.26

River: ($1.57) A (2 players)
UTG bets $1.57, MP raises to $4.27 all in, UTG calls $2.70

Final Pot: $10.11
UTG shows 2 Q (a flush, Ace high)
MP shows T K (three of a kind, Kings)
UTG wins $9.44
(Rake: $0.67)

What do you make of his shove on the river given that he held the Kc?

I would fold based on what you learned from the KT hand. if he overvalues trip kings ok kicker on a 3 flush board, there's no reason to believe he won't overvalue 6x or Qx if you were to shove.

The fact that you're shoving a "naked ace" means almost nothing. You're not getting him to fold a flush ever. Shoving a naked ace tends to be a better play against thinking villains in omaha because flush over flush is a much more common hand. So all you're doing is bluffing, and I don't think you can get him to fold any hand he's willing to pot into such a dangerous board on the river - just fold.

The shove in the second hand is also pretty ugly, with a bigger stack against a thinking villain you can rep the boat, but at 2-1 he's not going anywhere with a flush.

Why do you say that he's never folding a flush here? Even though it's a .02/.05 - .01 ante game the stacks are deep. He leads out for ~2/3 pot on the river and still has ~70BBs behind. He definitely folds some hands that he would bet like this and if he doesn't fold them to a shove we learn quite a bit and now have him playing ~200BBs deep and at this table we can buyin for that amount. It also gives us some table image to work with. I think this type of shove is generally a better play with some reads and I have no problem passing on it having just recently sat down. It's something to think about when you know that villain can't have the nut flush, although he could have a straight flush here I guess.