Things I like:
1) proactive company support for data security with the ability to request a database purge from users
2) clean and simple UI with a good font choice
3) detailed tutorials on how to use the app
Things that Need Improvement:
1) I'd suggest adding the "I reloaded", "I bought ammo", "I did maintenance" to a "home" screen, as that will make it easier for the home page to be a launchpad for "I did a thing" which makes it much easier to use as an ongoing concern. no paging through submenus, just open the app and hit the correct button
2) ammo should separate caliber and bullet type, this would make it easier to search by caliber and return a quantity breakdown of each general type (Poly Tip, soft point, FMJ, etc)
2) Optics should allow a "battery last replaced" date field
Other thoughts:
1) I'd suggest following the Garmin model of giving a 7-day free trial on first opening of the full feature set, as you are more likely to retain users when they have a period to discover how the app can work for them.
2) consider adding additional categories: Cleaning supplies, Batteries,
3) Ability to export locally stored information to a .CSV or other table format. this could be for several purposes, including for insurance purposes in the case of a total loss (flood/fire/tornado/etc)
4) Add a Date line to the "I shot today" log line, sometimes it's useful to know when something was *actually* last shot, as that can inform maintenance procedures (haven't shot something in X weeks - clean it and use a different CLP to prevent passive corrosion)
ADD A CANARY SIGN TO YOUR APP SOMEWHERE if you are unfamiliar with the concept:
https://en.wikipedia.org/wiki/Warrant_canary
The reasons for this should be obvious. while the actual firearm data may not be 'stored in the cloud' having such a thing would increase the trust an already highly skeptical and skittish user base would have in your services.