Extinguishing it, and shaping it with shape manipulation are two completely different things.
Sasuke was able to use shape manipulation on his Amaterasu and created his Blaze element, but at the same time it was also stated in his fight vs Danzo that he wasn't as good at using Tsukiyomi like Itachi.
This is what I'm thinking:
I think it's because Sasuke is more of a ninjutsu specialist and that's why he was able to use shape manipulation on Amaterasu and create Blaze Release. Itachi, while also good in ninjutsu, was more of a genjutsu specialist, and that's why he could use Tsukiyomi so well to the point of controlling space-time (72 hours in 1 second).
I think their own abilities gave them more control over the two techniques. Amaterasu is a ninjutsu technique, while Tsukiyomi is a genjutsu technique.
But to answer your question, Itachi was a genius prodigy that excelled at almost everything so it's very possible he could have. Obviously we can't know for sure if he could use Blaze Release, but personally I don't think he could. It's possible, but if he could then he would have used it in his fight against Sasuke. He was losing his eyesight anyways and he KNEW he was going to die so I don't see any reason for him to have held back on that.
He went full out and used everything he had in that fight to push Sasuke to his limits and to display the abilities of the Sharingan to Sasuke, so if he could then I think he would have.