Black Watch soldier Richard Scroggie, who has served in Iraq, Afghanistan, Kosovo and Northern Ireland, was found not guilty of offensive behaviour at a football match after he referred to Irish-born Flood as a "fenian" – a derogatory word for Catholics – at a Scottish Cup tie against Dundee United at Tannadice in February this year.
He was convicted of breach of the peace and fined £150 by Sheriff Kenneth Hogg.
Scroggie is free to continue attending matches after a proposal for a football banning order was rejected.
The sheriff also threw out an allegation Scroggie used foulmouthed language about the Pope and the Vatican. He described the legislation as confusing and difficult to wade through.
He said he was troubled and unimpressed by two officers from the Police Scotland Football Co-ordination Unit, FoCUS who gave evidence during the trial.
Sheriff Hogg said: "I wasn't impressed by their suggestion that Dundee United is a sectarian club. I've never heard that before in my life and the officer was trying to create that impression."
Scroggie's lawyer accused constables Adrian Kelly and John Brown, of the FoCUS unit, of lying that Scroggie had sang the offensive lines to Rangers song Follow Follow during the club's. The two officers told the trial that 20 minutes into the match they heard Scroggie shout out that Flood should go back to his former club, Celtic, as he was a "fenian".
Mr Brown said he issued Scroggie with a warning for the comments, which he admitted making. However, Scroggie denied singing the offensive lines from the Rangers terracing song Follow Follow.
Scroggie, 48, of Johnstone, Renfrewshire, was found not guilty of engaging in behaviour of a kind which is likely to incite public disorder by shouting, singing and chanting foul and abusive language of religious hatred.
Sheriff Hogg found him guilty of a breach of the peace by shouting language of religious hatred.
He said: "The section of the legislation you were charged under is very confusing. It is very unhelpful and until some appeals go through we won't get much guidance.
"There is a reasonable doubt about whether you sang Follow Follow, so that takes us back to your original remark only.
"I can't convict you under the Offensive Behaviour at Football legislation because I'm not convinced that one remark would be likely to cause public disorder."
Sentencing, Sheriff Hogg refused a Crown motion to impose a football banning order, but described the soldier's action as the "height of stupidity".
He added: "I still can't grasp why people shout this stuff – it has nothing to do with football and it has to stop."
Earlier this week, it was that revealed 268 charges had arisen from the Offensive Behaviour at Football and Threatening Communications (Scotland) Act 2012. Most of the incidents were for acts at football stadiums.