The "New-SelfSignedCertificate" in the else block no longer works with powershell v5 (and higher?):

$PspkiVersion = (Get-Module PSPKI).Version
if($PSPKIVersion.Major -ieq 3 -And $PspkiVersion.Minor -ieq 2 -And $PspkiVersion.Build -ieq 5) {
New-SelfsignedCertificateEx -Subject "CN=$DnsName" -EKU "Server Authentication", "Client authentication" -KeyUsage "KeyEncipherment, DigitalSignature" -Path $NewPfxFilePath -Password $securePassword -Exportable
}
else {
New-SelfSignedCertificate -CertStoreLocation Cert:\CurrentUser\My -DnsName $DnsName -Provider 'Microsoft Enhanced Cryptographic Provider v1.0' | Export-PfxCertificate -FilePath $NewPfxFilePath -Password $securePassword | Out-Null
}
We got it to work by removing "-Provider 'Microsoft Enhanced Cryptographic Provider v1.0'" from the New-SelfSignedCertificate line.

How to get connected to SF Cluster Endpoints from behind corporate proxy?
As I am getting below:
WARNING: Failed to contact Naming Service. Attempting to contact Failover Manager Service... WARNING: Failed to contact Failover Manager Service, Attempting to contact FMM... False WARNING: No connection could be made because the target machine actively refused it 40.117.45.185:19000 Connect-ServiceFabricCluster : No cluster endpoint is reachable, please check if there is connectivity/firewall/DNS issue. At line:1 char:1 + Connect-ServiceFabricCluster -ConnectionEndpoint mycluster.westus.cloudap ... + ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + CategoryInfo : InvalidOperation: (:) [Connect-ServiceFabricCluster], FabricException + FullyQualifiedErrorId : TestClusterConnectionErrorId,Microsoft.ServiceFabric.Powershell.ConnectCluster

Invoke-AddCertToKeyVault -SubscriptionId "xxxxxxxx-8cfb-4b8a-9c6f-4d1d5484852d" -ResourceGroupName "ServiceFabric_rg" -Location "eastus" -VaultName "sfkeyv2" -CertificateName "servicefabriccertificate1" -Password "Password@1234" -CreateSelfSignedCertificate -DnsName "www.appsfabric.eastus.cloudapp.azure.com" -OutputPath "C:\Certificate
recognized

Invoke-AddCertToKeyVault : The term 'New-AzureRmResourceGroup' is not recognized as the name of a cmdlet, function, script file, or operable program. Check the spelling
of the name, or if a path was included, verify that the path is correct and try again.
At line:1 char:1

• Invoke-AddCertToKeyVault -SubscriptionId "1428e18b-8cfb-4b8a-9c6f-4d1 ...

•   + CategoryInfo          : ObjectNotFound: (New-AzureRmResourceGroup:String) [Invoke-AddCertToKeyVault], CommandNotFoundException
    + FullyQualifiedErrorId : CommandNotFoundException,Invoke-AddCertToKeyVault
  

When attempting to import this on my Windows 10 laptop, I get the following error:

Add-Type : Could not load file or assembly
'file:///C:\users\tom.medhurst\Desktop\sfmodule\Scripts\ServiceFabricRPHelpers\System.Fabric.CSMTemplate\System.Fabric.CSMTemplate.dll' or
one of its dependencies. Operation is not supported. (Exception from HRESULT: 0x80131515)
At C:\users\tom.medhurst\Desktop\sfmodule\Scripts\ServiceFabricRPHelpers\ServiceFabricRPHelpers.psm1:11 char:1

• Add-Type -Path "$invocationDir\System.Fabric.CSMTemplate\System.Fabri ...

• - CategoryInfo          : NotSpecified: (:) [Add-Type], FileLoadException
  - FullyQualifiedErrorId : System.IO.FileLoadException,Microsoft.PowerShell.Commands.AddTypeCommand
  

I have downloaded the entire contents of the repo and have even tried an escalated powershell but neither seem to work.

The assembly exists, but there must be another dependency etc. that is missing?

Command ran:
import-module "C:\users\tom.medhurst\Desktop\sfmodule\Scripts\ServiceFabricRPHelpers\ServiceFabricRPHelpers.psm1"

New-AzureRmServiceFabricCluster : The primary certificate parameters names in the parameters file should be specified with 'sourceVaultValue','certificateThumbprint','certificateUrlValue', if the secondary certificate parameters are specified in the parameters file,
the parameters names should be specified with 'secSourceVaultValue','secCertificateThumbprint','secCertificateUrlValue'.
At line:1 char:1
+ New-AzureRmServiceFabricCluster -ResourceGroupName $resourceGroupName ...
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    + CategoryInfo          : CloseError: (:) [New-AzureRmServiceFabricCluster], PSArgumentException
    + FullyQualifiedErrorId : Microsoft.Azure.Commands.ServiceFabric.Commands.NewAzureRmServiceFabricCluster

After changing the parameters

  "clusterCertificateStorevalue": {
      "value": "My"
    },
    "clusterCertificateThumbprint": {
      "value": ""
    },
    "sourceVaultvalue": {
      "value": ""
    },
    "clusterCertificateUrlvalue": {
      "value": ""
    },

to:

   "certificateStorevalue": {
      "value": "My"
    },
    "certificateThumbprint": {
      "value": ""
    },
    "sourceVaultvalue": {
      "value": ""
    },
    "certificateUrlvalue": {
      "value": ""
    },

I get the error

New-AzureRmServiceFabricCluster : Code:DeploymentFailed, Message:At least one resource deployment operation failed. Please list deployment operations for details. Please see https://aka.ms/arm-debug for usage details. ,Details: Code:BadRequest, Message:{
  "error": {
    "code": "InvalidRequestFormat",
    "message": "Cannot parse the request.",
    "details": [
      {
        "code": "InvalidRequestFormat",
        "message": "The Thumbprint field is required."
      }
    ]
  }
} ,Details:
At line:1 char:1
+ New-AzureRmServiceFabricCluster -ResourceGroupName $resourceGroupName ...
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    + CategoryInfo          : NotSpecified: (:) [New-AzureRmServiceFabricCluster], Exception
    + FullyQualifiedErrorId : Microsoft.Azure.Commands.ServiceFabric.Commands.NewAzureRmServiceFabricCluster

New-AzureRmServiceFabricCluster : One or more errors occurred.
At line:1 char:1
+ New-AzureRmServiceFabricCluster -ResourceGroupName $resourceGroupName ...
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    + CategoryInfo          : CloseError: (:) [New-AzureRmServiceFabricCluster], AggregateException
    + FullyQualifiedErrorId : Microsoft.Azure.Commands.ServiceFabric.Commands.NewAzureRmServiceFabricCluster

5-VM-1-NodeTypes-SecureRP_ServiceCertValidationNone.json.txt
5-VM-1-NodeTypes-SecureRP_ServiceCertValidationNone.parameters.json.txt

The powershell command you created Invoke-AddCertToKeyVault has the following parameters to upload an existing certificate to KeyVault:

-UseExistingCertificate
-ExistingPfxFilePath

The Json blob you create even specifies dataType = 'pfx'

How would I modify this script to upload a certificate that does not contain a private key, e.g. a .cer file instead of a .pfx file?

Line 409
New-SelfSignedCertificate -CertStoreLocation Cert:\CurrentUser\My -DnsName $DnsName -Provider 'Microsoft Enhanced Cryptographic Provider v1.0' | Export-PfxCertificate -FilePath $NewPfxFilePath -Password $securePassword | Out-Null

results into an error:

Invoke-AddCertToKeyVault : A parameter cannot be found that matches parameter name 'Provider'.

I have been looking around and found only powershell scripts for ProviderName, but not out of the box.

I am getting this error. I am running the latest

It seems the latest PSPKI module has changed. New-SelfSignedCertificate is now New-SelfSignedCertificateEx

PSPKI Documentation for New-SelfSignedCertificateEx

This is probably more of a VSTS thing than ServiceFabric, however I was trying to execute your script from VSTS as an inline powershell task. I can clone your repo, import your module and execute the script. However I get an Access Denied in KeyVaultDataServiceClient.SetSecret. I have also gone to the KeyVault and added the Microsoft.VisualStudio.Online Application Name in the Access Policies. Will I have to interact with KeyVault in a different way if I am using a ServicePrincipal?