Trainer Kim Bailey says First Flow's next target will be the Ascot Chase and has praised his charge's performance in Saturday's Clarence House Chase.
The 10-year-old was hoping to defend his title after winning the Grade One in 2021, seven lengths clear of Politologue.
However, much of the build up was dedicated to the impending duel between Shishkin and Energumene — widely regarded as the biggest stars of the two-mile division.
Ultimately in Saturday's race, those two were the dominant duo with Shishkin taking the victory by one length from Willie Mullins' charge.
First Flow was a long way back in third, 19 lengths behind the winner, with Amoola Gold rounding out the field in fourth.
First Flow went into the race on the back of success in the Peterborough Chase at Huntingdon but couldn't keep up with the talent in front of him.
Nevertheless, Bailey was very happy with how his charge had performed with jockey David Bass believing it was a better display than 12 months ago.
Bailey also said a run in the Ascot Chase will be the next target for First Flow, with the race due to take place on February 19.
Bailey said: "It was a phenomenal race and David Bass said he ran a better race yesterday than he did last year, which gives you some idea how good the race was.
"It was a fantastic day for racing. As good a day's racing as we've had, all over from Haydock to Ascot and Taunton on TV, which was fantastic, and to see those two horses do what they did was phenomenal.
"He'll go to the Ascot Chase next month. He's fine this morning."
First Flow is also a likely entrant in the Queen Mother Champion Chase at Cheltenham Festival.
He finished sixth out of nine horses in the 2021 race, six-and-a-half lengths adrift of Put The Kettle On.
Shishkin — now unbeaten in his last 10 races — and Energumene are also looking to enter the Grade One Cheltenham race in a rematch of their Clarence House battle.