Is there a more specific term than 'flight line' for straight lines flown during flight?
Although my aviation knowledge is not all encompassing, I would argue that you, your boss, and your software company may want to know your audience as well as possible. The same terminology can mean different things to different segments of society. For instance, uncontrolled airspace/airfield would mean something totally different to a pilot than it would mean to the media or general public. 

A quick search of the Federal Aviation Regulations/Airmen’s Information Manual, the Pilots Handbook of Aeronautical Knowledge , and the Airplane Flying Handbook only garners results describing specific areas of an airfield and the personnel working there. My experience in civilian aviation and in the military is consistent with this usage. When pilots, ATC, and others in the aviation field describe an aircrafts path, they use terms such as the following:


Route
Return route
Round-robin route
Great circle route
Flight path
Leg
Direct leg
Course
Direct course
Track


The term you are probably looking for is Transect pattern consisting of transect lines.

Someone more knowledgeable might have a better term.