You may use Duration-Based Session Stickiness and just use ELB's cookie for sticky session. The session will expire according to "Expiration Period" set in the AWS or after browsing session is over if "Expiration Period" is left blank. Please set the Expiration Period according to your need (e.g. 60 minutes if you expect a user would not spend more than 60 minutes in Artifactory UI).
Or, you may use Application based Sticky Session method with JSESSIONID cookie as an application cookie, since Artifactory uses JSESSIONID cookie for UI authentication sessions. The session expires when browsing session is over.
For more information on setting AWS ELB Sticky session, please visit AWS's documentation page.
As an alternative, you may set the Artifactory SaaS HA's sticky session on nginx that you may setup behind AWS ELB, and simply setup sticky session by IP addresses of each HA node only for the Artifactory UI (/webapp), or you may setup cookie based sticky session using information here.