Have you gotten the app to work without the uidatepickers yet? I mean, are you able to load a file, select columns, and plot all of their data (without regard to the start/end date, just plotting all the selected columns' data)?
It doesn't work for me when I try it, so if I were you, I would get that working first and then try to get the uidatepickers working.
The problem I ran into is that table app.t's columns are all cell arrays of character vectors. You cannot plot a cell array; you'll either have to modify the readtable call to give you a table containing something you can plot, or convert the app.t's contents to some plottable class (numeric or datetime in this case) at some point - either when you first load the file or just before you plot.
