The simplest (but not necessarily the fastest) way I can think of is to open your entire file, convert it to array, and then take the last 8640 lines of your array using the "array subset" function.
Depending on the speed required for your application this might not be the most efficient way as large files (done multiple times) will slow your system.
Unfortunately, I dont think you can use the "Get lines from file.vi" to specify the number of lines and line offset to obtain your last 8640 lines.