I know at this time deletion of the run history (LogicApps) is not possible, on with a workaround with deletion recreation of the logicApp. And run history is now useable in the range of 7-90 days for keeping data.
(see other for that: Is there any way to delete logic app run history / logs? ).
But is alternative there a way to encrypt the data with a password or key, the apps can run and not everyone who has rights to this resource can see the data in the run history?
To store data like password and key, azure recommend us to use azure key vault. So I suggest you to use key vault store your password and key, and then get the key vault in your logic app. Please refer to the steps below:
1. Create a key vault account.
2. Then go to your key vault account and click "Secret" tab, click "Generate/Import" to create the secret and store the password value in it.
3. Go to your logic app, click "Identity" tab and enable the "Status"
4. Go back to key vault account, click "Access policies", click "Add Access Policy".
In next page, search your logic app name and add it (after this operation, your logic app can access the key vault secret).
5. Then back to your logic app designer. Use "Get secret" action of Azure Key Vault connector to get the value of "password1".
6. Click the
...button in the upper right corner of "Get secret" action, click "Settings".Enable "Secure Outputs".
7. After that, you can use the password value in your next actions and we can't see the password value in the run history.
8. Users can't see the value of secret in key vault account on portal if you don't assign permission for him. If user want to access the key vault, you need to do operation which similar with step 4 above(just change search the logic app name instead of search the user account, and add the user in it).