No, I don't believe you can do that with the app. I just looked at the app on my phone and I only see the option to launch or remove the channel. Move channel doesn't show on the app like it does on the TV screen. You can use the remote function of the app, but that's no easier/faster than using the Roku remote itself.
Dan
Roku Stick (3600), Ultra (4640), Ultra (4670), Ultra (4800), Premiere (3920), Insignia 720p Roku TV, Sharp 4K Roku TV, Nvidia Shield, Windows 10 Pro x64 running Serviio and Plex on a wired Gigabit network.