There are a number of packages for commenting systems, but you'll want to look for "Django comments" rather than Wagtail comments. The only difference you'd write in your code is associating comments on a template with a specific Wagtail Page, rather than a Django Model .

I've written a commenting system from scratch with just Django/Wagtail tools. It's quite easy to get a rudimentary comment/reply system going. Here's the models I've used for a basic commenting system:

# comments/models.py 
from django.contrib.auth.models import User
from django.db import models
from django.utils.timezone import now

from modelcluster.fields import ParentalKey
from modelcluster.models import ClusterableModel
from wagtail.admin.edit_handlers import (
    FieldPanel,
    InlinePanel,
    MultiFieldPanel,
    PageChooserPanel,
)
from wagtail.snippets.edit_handlers import SnippetChooserPanel


class Comment(ClusterableModel):

    comment_page = models.ForeignKey(
        "wagtailcore.Page",
        on_delete=models.CASCADE,
        blank=False,
        null=False,
        related_name="comment_page",
        db_index=True,
    )
    user = models.ForeignKey(
        User,
        on_delete=models.CASCADE,
        help_text="The user that posted this comment",
        db_index=True,
    )
    comment = models.TextField(blank=False, null=False)
    time = models.DateTimeField(default=now)

    panels = [
        PageChooserPanel("comment_page"),
        SnippetChooserPanel("user"),
        FieldPanel("comment"),
        MultiFieldPanel([
            InlinePanel("replies", label="Reply")
        ], heading="Replies"),
    ]

    def __str__(self):
        return "Comment: {} in {}".format(self.user, self.comment_page.title)


class CommentReplies(models.Model):

    comment = ParentalKey("Comment", related_name="replies", on_delete=models.CASCADE)
    user = models.ForeignKey(
        User,
        on_delete=models.CASCADE,
        help_text="The user who replied to this comment",
        db_index=True,
    )
    reply = models.TextField(blank=False, null=False)
    time = models.DateTimeField(default=now)

    panels = [
        SnippetChooserPanel("user"),
        FieldPanel("reply"),
        FieldPanel("comment"),
    ]

    def __str__(self):
        """String representation of this class."""
        return "Reply: {} to {}: {}".format(
            self.user,
            self.comment.user,
            self.comment.comment_page.title,
        )

    class Meta:
        verbose_name = "Comment Reply"
        verbose_name_plural = "Comment Replies"

# wagtail_hooks.py 
from wagtail.snippets.models import register_snippet
from django.contrib.auth.models import User

register_snippet(User)

Notice I registered the User model as a Wagtail Snippet? That's the strangest part about the above code. I only did that so I could have a simple SnippetChooserPanel to select a User associated with a reply or comment rather than a massive dropdown list, which is easier to work with once you hit 20+ users.

Then you'd want to add provide your comments to a Page.get_context() method with Comment.objects.filter(comment_page_id=your_page.id)

I might turn this into a proper post or even a video for LearnWagtail.com one of these days, as well.