Is there a way to use Azure Logic app to read an outlook email which has a link that dowloads a csv file and then store the file in a storage blob?
Yes, you can do by following below design:

Then:

Get Attachement (V2)2:

Then:

Full design:

Created a storage account:

After new emails comes with attachment:

Now logic app runs:
In storage account after logic apps runs:


Code View :
{
"definition": {
"$schema": "https://schema.management.azure.com/providers/Microsoft.Logic/schemas/2016-06-01/workflowdefinition.json#",
"actions": {
"For_each": {
"actions": {
"Create_blob_(V2)_2": {
"inputs": {
"body": "@base64ToBinary(body('Get_Attachment_(V2)_2')?['contentBytes'])",
"headers": {
"ReadFileMetadataFromServer": true
},
"host": {
"connection": {
"name": "@parameters('$connections')['azureblob']['connectionId']"
}
},
"method": "post",
"path": "/v2/datasets/@{encodeURIComponent(encodeURIComponent('AccountNameFromSettings'))}/files",
"queries": {
"folderPath": "/rithwik",
"name": "@body('Get_Attachment_(V2)_2')?['name']",
"queryParametersSingleEncoded": true
}
},
"runAfter": {
"Get_Attachment_(V2)_2": [
"Succeeded"
]
},
"runtimeConfiguration": {
"contentTransfer": {
"transferMode": "Chunked"
}
},
"type": "ApiConnection"
},
"Get_Attachment_(V2)_2": {
"inputs": {
"host": {
"connection": {
"name": "@parameters('$connections')['office365']['connectionId']"
}
},
"method": "get",
"path": "/codeless/v1.0/me/messages/@{encodeURIComponent(triggerBody()?['id'])}/attachments/@{encodeURIComponent(items('For_each')?['id'])}"
},
"runAfter": {},
"type": "ApiConnection"
}
},
"foreach": "@triggerBody()?['attachments']",
"runAfter": {},
"type": "Foreach"
}
},
"contentVersion": "1.0.0.0",
"outputs": {},
"parameters": {
"$connections": {
"defaultValue": {},
"type": "Object"
}
},
"triggers": {
"When_a_new_email_arrives_(V3)": {
"inputs": {
"fetch": {
"method": "get",
"pathTemplate": {
"template": "/v3/Mail/OnNewEmail"
},
"queries": {
"fetchOnlyWithAttachment": true,
"folderPath": "Inbox",
"importance": "Any",
"includeAttachments": false
}
},
"host": {
"connection": {
"name": "@parameters('$connections')['office365']['connectionId']"
}
},
"subscribe": {
"body": {
"NotificationUrl": "@{listCallbackUrl()}"
},
"method": "post",
"pathTemplate": {
"template": "/GraphMailSubscriptionPoke/$subscriptions"
},
"queries": {
"fetchOnlyWithAttachment": true,
"folderPath": "Inbox",
"importance": "Any"
}
}
},
"splitOn": "@triggerBody()?['value']",
"type": "ApiConnectionNotification"
}
}
},
"parameters": {
"$connections": {
"value": {
"azureblob": {
"connectionId": "/subscriptions/b83c1b83a/resourceGroups/v-rbojja-Mindtree/providers/Microsoft.Web/connections/azureblob",
"connectionName": "azureblob",
"id": "/subscriptions/b83c1c2/providers/Microsoft.Web/locations/eastus/managedApis/azureblob"
},
"office365": {
"connectionId": "/subscriptions/b83c1ed3-/resourceGroups/bojja/providers/Microsoft.Web/connections/office365",
"connectionName": "office365",
"id": "/subscriptions/b83f/providers/Microsoft.Web/locations/eastus/managedApis/office365"
}
}
}
}
}