Because I consider Infowars to be a less reliable source than my cats (who always say they're hungry and are always correct), I spent an hour or so going through the edit history of the Wikipedia article on American Airlines, page by page, using my browser's "find" function to look for any IPs in the 144.9.x.x block, which belongs to AA.
Eventually I did find the edit in question. The verbiage about the BTS database was added at 1845 UTC on May 5, 2006 by 144.9.8.21. It was removed about a month later by user Maverick05, with the comment "This is stupid and offensive. Keep conspiracy theories to their own pages.".
Since then, 144.9.8.21 has made some nine edits to the same article- none of them having anything whatsoever to do with 9/11. They have instead been trivia about the addition of winglets, corrections to the list of AA's partner airlines, and other things which a knowledgeable employee might be motivated to correct in an article about their workplace. Since 144.9.8.21 is very likely a gateway IP for an entire office (or building) we can't infer that all of these were made by the same person.
There has been, as far as I can determine, no attempt at all to put that text back in the Wiki article. These circumstances don't suggest that it was an official company position nor a genuine whistleblower. What they do suggest is some bored office dweeb who had internet access via the company network and used it to waste time reading conspiraloon Web sites.
Turning to the BTS database itself, I find this:
Airline on-time data are reported each month to the U.S. Department of Transportation (DOT), Bureau of Transportation Statistics (BTS) by the 18 U.S. air carriers that have at least 1 percent of total domestic scheduled-service passenger revenues, plus two other carriers that report voluntarily. The data cover nonstop scheduled-service flights between points within the United States (including territories) as described in 14 CFR Part 234 of DOT's regulations.
Sauce
That an airline in the straits that AA was in after 9/11 could neglect reporting the on-time takeoff of the two worst disasters in their history is something that only a dedicated conspiracist can see as suspicious, or as having any evidentiary value at all.
When I see just how determined people like AJ are to perceive boogeymen behind every blade of grass, I marvel that they ever manage to walk to the bathroom without dying of fright.