So, starting from the beginning it is not till now clear that is Dabi Endeavor's Son or not? but their is a speculation about this due to the fact that Endeavor and Shouto both have kind of weird moments with Dabi. It would be only possible if they both knew Dabi and if not then there are certain moments which will be complete bizzare. So, there is a possibility they know each other.
Another speculation is that without Dabi's fire power or marks on his body as his body is not developed perfectly to handle the ability it is definitely a fact and Endeavor seems to notice that too. He may have similar genetic structure that can also be the case. But it is not a coincidence that Dabi's physical appearance as well as his sharp eyeline very much resembles to that of Shoto.
For another similarities he also possess same blue eyes and as well as he is also tall as compared to Shoto which also points out to the fact that Dabi may be Endeavor's Son. And the most important trait being his fire quirk which strongly resembles to that of Shoto is another fact that can't be ingnored.
The motivations that he have also indicates to the point that Dabi is also a Todoroki. He is follower of Hero Killer Stain which may be due to the Endeavor's extensive training that he does in order to make his son better than All might.
Thus after witnessing abuse daily on him as well as his mother and on the two siblings Dabi started to hate Hero society. As he thought instead of saving someone's life heroes only care about their own prestige. So, with these facts we can somehoe believe that Dabi is Endeavor's son.
Why are Dabi's Burn scar purple instead of being red like Todoroki?
Dabi's burn is not something which is caused due to any incident or fight but these scars he got from his mother when he was born. So, when she saw his scars she tried to treat those burns with her quirk after putting boiling water on his face. But, it resulted in a red burn. Dabi's scar situation is known as hypertrophic, which refers to when instead of scar being only on the skin it effects bones too thus causing itchiness in Dabi we many times saw. Scars are extended to the bone and whenever Dabi uses flame it causes itchiness. Dabi's scar are something that were caused by dry heat as compared to Shoto.
If people think Dabi is Todoroki, shouldn’t he have red flames instead of blue?
Manga spoilers ahead!
As we have reached a point where we know about many things and it is very hard to argue about the fact that Dabi is Touya. In one chapter of the manga we get to see that Touya have greater fire realted powers as compared to Endavor. As we see that Dabi's flames which are blue in color are more powerful when we compared it to Endeavor. And in front of Shouto too he have greater fire power.
Dabi's blue flames indicate that his flames are more hotter as compared to that of Endavor and Shouto. In the one chapter of manga we can see that Dabi is not able to fully control his flame like Endeavor can do. So, he is still lackimg in this part. Touya also is very similar to Dabi as he also can't control his flames and this was the point with Endeavor said about Touya.
We kow to some degree that Endeavor is also not very well versed in controlling is flames as he gets overheated whenever he uses his quirk for a longer period of time, but he have one advantage here which is his body can handle this as his body have been adapted in such way. If we think about Dabi and Touya if they are able to fully control their quirk than they will be too powerful and if Toya is able to fully control his fire and ice quirk than it will be very exciting for the viewers
Well the family of Endeavor also blames him for one thing about Toya mainly about the burns that he got. This happened due to Endeavor being to excessive in teaching the technique to Shouto which he said that only he is able to master it. Which ultimately resulted in the scars that he received. So, the family started to blame Endeavor for that.
Endeavor wanted Shouto to learn blue flames but without having ny drawbacks of using the technique which Dabi got oftenly. He thought that one day maybe Shouto will surpass him as he is the only one to learn the technique. It is also one speculation that Dabi is actually Touya. The character daruma ujiko did some experiments on Dabi's body and installed a new conciousness in him.
However he didn't achieved the desired results amd it was still incomplete as whenever Dabi tries too hard on something and overuse his powers he starts to bleed which means that their is somewhat problem with Dabi which can also linked with this speculation that Dabi is created by Daruma. And he is Daruma's incomplete creation. But it is still not a problem for Dabi as he can still use his powers perfectly and is still threat to many heroes which includes Endeavor, Hawk as well as Miriko. So, he is still a very dangerous character in My Hero Academia universe.
It can also not be neglected that there is still a possibility that Dabi is Touya.