@Prashantha Hosapattana Which all permissions you are looking for ? It is possible through REST API though you can use a PowerShell script like below to get all roles and assigned members if you are looking for the same.
[Reflection.Assembly]::LoadWithPartialName("Microsoft.AnalysisServices")
$ServerName = "asazure://westus2.asazure.windows.net/<servername>"
$DB = "adventureworks"
$MyServer = New-Object Microsoft.AnalysisServices.Server
$MyServer.Connect($ServerName)
$myDatabase = $myServer.Databases.Item($DB)
foreach ( $roles in $myDatabase.Model.Roles) {
foreach ( $role in $roles) {
Write-Output $role.Name
Write-Output "----------------------"
foreach ( $member in $roles.Members) {
"Member Name: " + $member.Name
Write-Output "`n"
}
Write-Output "`n"
}
}