The Graph Inbox rule endpoint only provides a subset of the full rules action that you can do in either the Outlook desktop client or Outlook on the web. So in your example using
"flag": {
"flagStatus": "flagged",
"flagColor": "#FF0000"
},
the flag action isn't available in the Graph API in v1.0 or beta the documentation list the available actions https://learn.microsoft.com/en-us/graph/api/resources/messageruleactions?view=graph-rest-1.0 or if you check it MessageruleActions in the metadata eg
<ComplexType Name="messageRuleActions">
<Property Name="assignCategories" Type="Collection(Edm.String)"/>
<Property Name="copyToFolder" Type="Edm.String"/>
<Property Name="delete" Type="Edm.Boolean"/>
<Property Name="forwardAsAttachmentTo" Type="Collection(graph.recipient)"/>
<Property Name="forwardTo" Type="Collection(graph.recipient)"/>
<Property Name="markAsRead" Type="Edm.Boolean"/>
<Property Name="markImportance" Type="graph.importance"/>
<Property Name="moveToFolder" Type="Edm.String"/>
<Property Name="permanentDelete" Type="Edm.Boolean"/>
<Property Name="redirectTo" Type="Collection(graph.recipient)"/>
<Property Name="stopProcessingRules" Type="Edm.Boolean"/>
</ComplexType>
EWS also doesn't support that action https://learn.microsoft.com/en-us/exchange/client-developer/web-service-reference/actions . The only Exchange API that does would be Mapi through the Tag action https://www.dimastr.com/redemption/rdo/rdoruleaction.htm#RDORuleActionTag
Otherwise look at subscriptions and build an app to modify the item.