Who can access a brand's store(s)?

All your teammates figuring on 'Manage Team' on the 'Edit my Store' tab can access your store.
If you'd like to add additional people to manage your brand store (create a product, a campaign, answer influencer requests, check campaign reports, etc...), click on 'Edit store' and then 'Manage Team'.  There you can invite your teammates who will receive their own user access via email.