From my small experiments it seems that this field isn't queryable through the Tooling API.
Using this query here:
https://www.salesforce.com/services/data/v40.0/tooling/query?q=Select+Id,+DeveloperName,+inlineHelpText+from+FieldDefinition+where QualifiedApiName='Account'
This returns
[
{
"message": "\nSelect Id, DeveloperName, inlineHelpText from FieldDefinition\n ^\nERROR at Row:1:Column:27\nNo such column 'inlineHelpText' on entity 'FieldDefinition'. If you are attempting to use a custom field, be sure to append the '__c' after the custom field name. Please reference your WSDL or the describe call for the appropriate names.",
"errorCode": "INVALID_FIELD"
}
]
Skipping the inLineHelpText from the query returns results so it seems that I can't retrieve this field data. Has anyone run into this problem?