This was mentioned in commentary on their game against Fulham. It wasn't too clear what was meant, but apparently in the entire history of the FA Cup Kettering have scored more goals than anyone else. I've not discovered the source of this, but I saw a post from a Kettering fan state that they had scored 830 with Aston Villa next best on about 800.
So the first thing to consider was how many had Reading scored, given that we've been entering longer than either of those two clubs. I did a rough check and came up with about 580. In 122 seasons that's pretty poor, even allowing for the currentl policy of scoring as few as possible each year.
Typically in any one season, the leading scorers in the FA Cup are a non-league club who played a lot of qualifying round matches, so I imagine that the way to be all-time leading scorers is to be a club who regularly is strong compared with others at the same level. Without knowing much of their history it's not too difficult to believe that this could apply to Kettering, but really it should also apply to Reading with all those years spent near the top of the third tier. We also have the benefit of large early round wins in the 19th century to add in.