Yesterday I got an email from Delta that says you can now access SkyMiles Dining from your Fly Delta app (for both Android and Apple). It says:
From the Fly Delta app's welcome page, select the "Traveling with Delta" option.
Choose "Delta Partners" from the page menu.
[One of the partners listed is SkyMiles Dining.] Select "Learn More" to access the SkyMiles Dining feature.