The SFA banned Jones for two games for diving to win a penalty in the club's 2-1 victory away at Dundee earlier in October.
Kilmarnock chose not to appeal against the verdict as they had insufficient evidence to prove Jones' innocence.
In response to correspondence from the Dundee Supporters' Association (DSA) questioning the suitability of Steven McLean to take charge of Kilmarnock matches, Fleming stated that the Rugby Park outfit accepted "the player committed the act, solely to deceive the referee".
"We made it clear that Jordan denied committing an act of simulation and denied any intention to deceive the referee," a statement read.
"The sole reason for not challenging the charge was that we had no additional substantive evidence so took a pragmatic view to accept the penalty and move on.
"Having taken this decision and accepted the penalty, we expected this matter to be closed.
"A formal complaint has been submitted to the SFA and we expect the matter to be investigated fully."