You need to make the fullname variable a property variable, so that it can be used by the different functions within the app.
Once this is done, you can reference the variable as such:
However, from the looks of your code, it seems you would want to load an image and fullname would represent the entire path to the image file. In this case, I would read the image file and use a properties variable for the image matrix.
app.fullname = fullfile(filepath,filename);
app.Image.ImageSource = app.fullname;
app.ImageMatrix = imread(app.fullname);
For the function imshow, you would need to specify a uiaxes in the app to display the image. You will need to make sure a uiaxes is present on your app's canvas (uifigure). Also, the image matrix needs to be the input and not a string of the file path.
function ImageClicked(app, event)
imshow(app.ImageMatrix,'Parent',app.UIAxes)
For the flipped image horizontally regardless of image size:
flipp = app.ImageMatrix(:,size(app.ImageMatrix,2):-1:1)
or
flipp = flip(app.ImageMatrix,2)
to display flipped image:
imshow(flipp,'Parent',app.UIAxes)