I have set-up private ACR set up with public access and admin credentials disabled.

It has a private endpoint approved ,setup with private connection,private dns zones configured.

The private endpoints reside in subnetEndpoint in virtualNetwork vNetApp
I have setup a DevOps pipeline using
agent pool. The agent makes use of a Virtual Machine scale set deployed in a virtual network agentSubnet in vNetApp.
The agent makes use of Service Principal which i have assigned acrPush role
The pipeline executes a docker build and should push the image to the private ACR with private endpoint.
I create a service connection dockerConn for connecting the Docker task to ACR 
I give dockerConn Acrpush role against the registry and pass it to the pipeline.
stage: Build
pool:
name: ${pool}
jobs:
- job: Build
displayName: Build
pool:
vmImage: $(vmImageName)
steps:
- task: Docker@2
displayName: Build and push an image to container registry
inputs:
command: buildAndPush
repository: $(acrImageRepository)-$(Build.SourceBranchName)
dockerfile: $(dockerfilePath)
containerRegistry: $(dockerRegistryServiceConnection) //This is given acrPush role
When i run the pipeline the Docker task fails when the step comes to push the image to ACR.
518047573282: Waiting
denied: client with IP '2.413.62.52' is not allowed access. Refer https://aka.ms/acr/firewall to grant access.
##[debug]Exit code 1 received from tool '/usr/bin/docker'
##[debug]STDIO streams have closed for tool '/usr/bin/docker'
##[error]denied: client with IP '2.413.62.52' is not allowed access. Refer https://aka.ms/acr/firewall to grant access.
##[debug]Processed: ##vso[task.issue type=error;]denied: client with IP '2.413.62.52' is not allowed access. Refer https://aka.ms/acr/firewall to grant access.
##[debug]Trying to logout from registry: ***
####[debug]set DOCKER_CONFIG=
##[debug]Processed: ##vso[task.setvariable variable=DOCKER_CONFIG;isOutput=false;issecret=false;]
##[debug]task result: Failed
##[error]The process '/usr/bin/docker' failed with exit code 1
error message:
client with IP '2.413.62.52' is not allowed access. Refer https://aka.ms/acr/firewall to grant access
The virtual network has the correct DNS Zones set up
Update:
also i created a vm in the same subnet as the VMSS . I was able to do confirming the private dns is setup correctly
nslookup myazurereg.azurecr.io
Server:127.0.0.53
Address:127.0.0.53#53
Non-authoritative answer:
myazurereg.azurecr.io
canonical name = myazurereg.privatelink.azurecr.io.
Name: myazurereg.privatelink.azurecr.io
Address: 12.101.3.5
Can anyone help here? Thanks
It looks like your vmss doesn't leverage 168.63.129.16 to resolve private endpoint URL. You may connect to your vm and append the line "nameserver 168.63.129.16" to the /etc/resolv.conf file.