Updated
Blitz does not import items, runes or spells automatically.
Please note: In order to be able to use the auto importing feature you must be at-least summoner level 10 or higher, we can't import runes/spells you are below level 10.
Step 1
Ensure that you have your preferred importing features enabled under Settings > League of Legends > Champion Selection.
If not resolved Step 1:
Make sure you are on the latest version.
You can check if an update is available under Settings > General > Application > Check for updates.
Step 2:
Ensure that you have at least 1 rune page available for Blitz. Otherwise it won't be able to import any runes.
If the previous steps did not fix your issue, please consider a clean re-installation. A step by step manual for that is available here.