Edit 2: I did PvP calculations in the #14th post and PvE calculations in the #72nd post.
If you don't know about the new Shadowburn's potential, let me tell you:
-1 Shadowburn costs 1 Soul Shard, 1 Chaos Bolt costs 2 Soul Shards. We'll start combat with only 1 Soul Shard in Legion, in Alpha at least. Max Soul Shards will be 5.
-2 Shadowburns hit for %680 spell dmg and 1 Chaos Bolt hits for %275 spell dmg with a guaranteed crit. Since we don't have "Dark Soul" anymore, CB won't be overpowered as much as before. Btw, CB is getting buffed by %20.
-Chaos Bolt's cast time will be 3 secs, but a PvP talent will make CB's cast time 2.5 secs. With "Backdraft" talent and "Improved Backdraft" talent, the cast time will be reduced by half, it means 1.25 secs cast time. With your base Haste(Averagely %7 right now for Destro in WoD) and the haste PvP talent(Increases %7 by %15=8,05), the cast time will be 1,15 secs. Pretty slick. However, you may want to pick the crit talent instead of haste, because %1,05 haste sucks.
-Average Crit chance for Destro is %17. The crit damage will probably stay %150 in PvP. So, 1 Chaos Bolt's dmg will be %482 spell dmg, without any buffs.
-2 Shadowburns without critting hits for %680, 1 Chaos Bolt hits for %482. Note that SB is instant. %198 more dmg with SB.
-Even if CB's cast time will be 1,15 secs, the GCD won't be that low. When you finish casting your CB, you gotta wait for the gap between 1,15 secs and GCD. So, the only moment CB hits more is at the first CB hit and before the 2nd SB comes. What I mean is, when you land 1 Chaos Bolt, it hits for %482 dmg. 1 SB hits for %340. Even if CB wins at the first hit, 1 SB would already hit the target before CB hits. By the time you start the casting your 2nd Chaos Bolt, already 1 SB would be landed and the other SB would be on the way. When you finish the 2nd CB, 2nd SB hit already and the 3rd SB will be on the way. SB costs lower than CB and a SB goes faster than a Chaos Bolt. Shadowburn wins here.
-The only time you can freecast will be with Mortal Coil, since Shadowfury is dead, you would wanna spend that time with Channel Demonfire. If you wanna cast CB at that moment, you would land max 2 CBs + 1 Conf in 3 secs = %1454,06 spell dmg with Mana Tap and Eradication. 1 Channel Demonfire with Mana Tap and without Eradication hits for = %1,725. Btw, you keep all of your Soul Shards with Channel Demonfire.
-With Shadowburn, you won't need Incinerate too. Incinerate won't give you any Soul Shards. Since you didn't pick Backdraft, the cast time will be higher. I'll give you an example of an opener in Legion = Mana Tap + Havoc + Conf + Immolate + Mortal Coil + Channel Demonfire + Havoc + SB + SB + SB + Conf + SB + SB. There is no guarantee that you'll do this opening, because of the CCs. After this, if you couldn't kill them, you'll cast Soul Harvest and continue spamming SB. Your filler will be Drain Life, not Incinerate, because you probably won't be at %100 all the time. If you want, cast Incinerate, but Incinerate is so worthless in Legion. I'd prefer Immolate and Channel Demonfire as fillers if you don't need heals. Havoc, Immo, CD, Fear and SB will surely keep you busy while you wait for Conf's cooldown to end.
-If you pick Eradication talent and decide to spam SBs after you land 1 CB, it's still not worth to cast 1 CB. You will be able to cast 3 SBs+1 Conf in 6 secs or 1 more SB if we add GCD reduction with haste. 4 SBs with %20 buff = 4,8 SBs. In the same period of time, you would cast 6 SBs+1 Conf.
Without SB crits and buffs
1 CB+4,8 SBs > 6 SBs
(%2114 spell dmg) (%2040 spell dmg)
It means you would sacrifice Soul Harvest or Cataclysm for %74 spell dmg. Shadowburn just destroys CB in both PvP and PvE.
TL : DR = You won't need Chaos Bolt in Legion. Read above to see how.
Edit: I was talking about PvP, but I think SB will even hit more than CB in raids too, because of the fewer Soul Shard cost. Only in the long run tho, since crit dmg is %200 in PvE. This will work in Instances too, due to 1 Soul Shard to cast and refunds 2 Soul Shards. Spamming SBs, gg.