The incident occurred in the 71st minute of his side's League Two clash with AFC Wimbledon on March 19 of this year.
The 30-year-old denied the charge, but has been found guilty by the FA and will now miss his side's next five outings.
"The player was alleged to have used abusive and/or insulting words contrary to Rule E3(1)," read a statement from the FA.
"It was further alleged that this was an 'aggravated breach' as defined by Rule E3(2) as it included a reference to ethnic origin and/or colour and/or race.
"The charge, which the player denied, was found proven following an Independent Regulatory Commission."
Flinders was also fined £1,250, warned about his future conduct and must complete an education course.