Now, I see some help very clearly showing. It seems there are consistent tenses and such, like ways of description that are both enjoyable and smooth in mental and vocal rehearsal. I noticed a strange lack of variations when it came to common words, however, like 'says' or 'smiled'. I commend your sparse use of words both multisyllabic and generally melodic like 'myriad' and 'mismatch'. Though, when the reader finds frequent verbs, like the infamous 'says' and 'smiles' like high-brow authors like avoiding, it can be jading. More than likely, the people giving you downvotes are clearly a bit more picky with diction and infrequent spelling mistakes throughout the first and preceding chapters.

This intrigued me and I generally did read the first chapter no fuss at all. I recommend whipping your editors' asses and bouncing editing off them. Like alternative solutions to proclaiming a character's vocal action, there are many, many words at your disposal. 'Says' can become 'suggests' and smiles can become 'upward lip tilt'. There are all sorts of miscellaneous solutions you can totally get behind, and you'll feel proud of reinforcing the little, but unappreciated details.

Also. I very much don't Like Sword Art Online, so, I didn't like it because of the crossover. I just enjoyed the writing and imagery.

Oh, and people will complain about the asterisk actions. I myself don't mind because I used to be a large RP person. That sort of thing is common there, but people expect a great epic of modern flow and novel description. So, less like Earnest Hemmingway's "A Farewell to Arms" and more like... well, a very clever, charming professional over a macbook. So, try and make the actions or events without asterisks, but more third-person narrative? It'll ease the flow amazingly well. Well enough for you to write stories like wildfire.

In a large brick lodging, in the center of a village during its annual celebration, a red dragon sleeps during the festivities,she & a large black egg clutched in her arms pressed to her ample chest lightly glowing red, her wavy white spines making no movement as she slumbers.

I like how this sounds but as a sentence its too long.
You need to break up the sentence.

she and a large
I am not sure lodging works, could you try building or castle?

I could see readers wondering what a lodging is.
To help with flow, you need to avoid stuff that will make readers stop and break immersion to understand words.

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The baby dragon is a small and purple with rounded emerald green spines , the same color as her eyes and lacks wings like the dragoness before her, her green frills at the side of her head are angled down as she approaches the sleeping dragon and lightly shaking her shoulder to wake her up.

You need to break this sentence up too.
I suggest one thought per sentence, that makes it easier to follow.

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“Mom, can you tell us a story while we wait?” asks Barb innocently, the elder of the pair, a pink filly sits waiting expectantly(.)

Watch out for weird spacing and missing punctuation.

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“Of course,” answers the dragon smiling sweetly, her voice melodic, she places the egg in front of her and places Barb on her left(.)

Who is Barb?
Yeah, I can guess but its much better if you just explicitly said who Barb is and what she looks like.

You use place twice in the sentence, that can get boring.

This might be better:
she places the egg in front of her and motions to Barb to sit next to it.

Tense issues

she placed the egg in front of her and motioned to Barb to sit next to it.
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“Come over here Screwball,(sp)you’ll wanna hear too,” beckoning her closer.(s)Screwball smiles and goes over, placing herself on the right side of her mother, snuggling in close.

Who is Screwball?
Does this contradict the earlier sentence where Barb sits next to the egg?

“I guess you could say it all began with the fall of the empire.

We don’t know too much of how it happened or why it occurred, even our oldest living elders have no idea, all we do know comes from the surviving relics we hold from those days , the old scrolls and books.

We only know that it was a tragedy and took many lives but we, the clans and others, were the survivors.”

Uppercase Empire.
You use we a lot and that can get boring.

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“The clans are each known as: Incendia, Naga, Ark, Titan, Razor, Styx, and us the Loki. The clans were not always in tune with one another, my children there was once much violence among us.”

This works fine but I think you could make it more interesting by adding a line about each clan. This will help with worldbuilding.

The clans are each known as:
Incendia, masters of flame.
Naga, master of poisons and exlixirs.
etc

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“Well(,) personally I don’t know why there was so much fighting among us; the fighting had being going on long before I was hatched, none of us even remember what started the fighting .”

formatting issues.

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Redmoon shrugs her shoulders as she tries to remember why they all fought, she decides to tell her daughters.

You do not have to say what she shrugs.

Who is Redmoon?
You probably should have said who she was earlier in the story.

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“Now then my little ones, this will more of a tale of how each of you came into this world and how we came to be what we are so it will involve a bit of history(,)” she says with a smile.

said
Most stories are told in past tense.

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What I have read sounds interesting.
I think the formatting and punctuation errors are making people give you downvotes.

I will come back and finish this chapter.