DOM-based vulnerabilities arise when a client-side script reads data from a controllable part of the DOM (for example, the URL) and processes this data in an unsafe way.
Client-side SQL injection arises when a script incorporates controllable data into a client-side SQL query in an unsafe way. An attacker may be able to use the vulnerability to construct a URL that, if visited by another application user, will execute an arbitrary SQL query within the local SQL database of the user's browser.
The potential impact of the vulnerability depends on the application's usage of the SQL database. If the database is used to store sensitive data (such as messages in a social networking application), then the attacker may be able to retrieve this data. If the database is used to store pending user actions (such as outgoing messages in an email application), then the attacker may be able to modify this data and carry out actions on the user's behalf.
Burp Suite automatically identifies this issue using static code analysis, which may lead to false positives that are not actually exploitable. The relevant code and execution paths should be reviewed to determine whether this vulnerability is indeed present, or whether mitigations are in place that would prevent exploitation.