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I'm trying to make a Sarkhan's Unsealing deck using G/R. How does the interaction work with Fling if say;

• I play a creature


• The creature is targeted by removal when entering (Murder, Ixalan's Binding, Essence Scatter)


• I play Fling sacrificing my creature

Does the damage from Fling get priority and complete the action?

It sounds like you're confused or have misconceptions about how spells are cast and resolved. That's fundamental to this issue so I suggest you read this answer about how casting and the stack works. Go check it out now, then come back here. The following will make more sense once you've done that.

Let's first go through how this scenario plays out before we add Fling or removal:

1. You cast your creature. In doing so, you put it on the stack. It's now a spell in the stack zone.


2. One of the triggered abilities of Sarkhan's Unsealing triggers. We put that triggered ability on the stack. If it's the first ability you choose its target whilst doing this. The stack now looks like this:
   
   
   • Sarkhan's Unsealing triggered ability (top)
   
   
   • Your creature (bottom)
   
   


3. Sarkhan's Unsealing's triggered ability resolves, dealing its damage.


4. Your creature resolves, and then enters the battlefield.

OK, so, let's add to this:

• Effects that reference a "creature" (not "creature card" or "creature spell") exclusively reference a creature permanent (card or token) on the battlefield.


• Effects that reference a "creature spell" exclusively reference a creature card on the stack.

This means Fling, Murder, and Ixalan's Binding can only target your creature after step 4, once it's on the battlefield. Essence Scatter can only target your creature whilst it's a creature spell on the stack, i.e. after step 1 and before step 4.

So what happens when we add those in?

• 
  Essence Scatter: Your opponent can cast this spell after you finish casting your creature. They cannot cast it before step 2, because they do not receive priority yet. They can counter your creature, but they cannot counter Sarkhan's Undoing nor stop it resolving. You'll deal your damage. You cannot Fling your creature in this scenario because it is not on the battlefield, it's on the stack.


• 
  Murder: They can cast this only after step 4. You will already have your creature on the battlefield and the damage will have been dealt. You can cast Fling in response, and sacrifice it to deal damage.


• 
  Ixalan's Binding is similar to Murder: they cast the spell, it enters the battlefield, its ability triggers targeting your creature, and then you can Fling your creature in response. However note they can't do this in response while it's your turn: Ixalan's Binding isn't an instant and doesn't have flash.

I believe there are possibilities not covered by the existing answers, so I will make my own covering the possible interactions.

Essense Scatter and Fling

Essence Scatter and Fling will not interact. Essence Scatter targets a "creature spell" while Fling sacrifices a "creature". Although both use the word "creature", it is impossible for something to be both a "creature spell" and a "creature" at once. There is no way to Fling a creature that is being Essence Scattered.

Murder and Fling

Fling can be cast in response to Murder, and sacrifice the creature targeted by Murder. If no other effects are involved, Fling will sacrifice the creature and deal the expected damage, then Murder will have no effect because it no longer has a target.

Ixalan's Binding and Fling

Mostly, Ixalan's Binding works the same as Murder, but the timing is different. Ixalan's Binding as a spell does not have a target at all. If Fling is cast in response to Ixalan's Binding being cast, then Fling will resolve normally but where Murder had no effect Ixalan's Binding would still resolve. It would then enter the battlefield and its trigger would be free to exile a different creature. If the Ixalan's Binding enters the battlefield, then Fling can instead be cast in response to that triggered ability; if so, then the Fling (again) resolves normally and the triggered ability would have no effect. In this case Ixalan's Binding would remain on the battlefield but would not exile anything.

Fling and Murder

Not specifically mentioned in the question, but changing the order of spells in this case is different from most cases where spells are cast in the opposite order. Spells resolve "Last In - First Out", which means a Murder cast after a Fling would resolve before the Fling. However, the result might not be as you would expect. Fling includes the phrase "As an additional cost to cast this spell". The listed cost for this phrase, "sacrifice a creature", happens when the spell is cast, unlike the rest of the text which happens when the spell resolves. The net effect here is that, although Fling can stop a Murder by removing its target, Murder cannot stop a Fling by removing its sacrifice. If Fling is cast before Murder, then Murder cannot even be cast unless it targets a different creature.

Fling and a different counter spell

Although Essence Scatter cannot interact with Fling, other counters can. If Fling is cast, and then a Cancel is cast targeting that Fling, then the interaction is again somewhat different. Normally a counter spell would stop all the effects of whatever it counters. However, as noted above, Fling sacrifices a creature "as an additional cost" not as part of the effect. The result is that Fling will still sacrifice the creature even if it is countered and deals no damage.

The interaction with Murder is very different than the interaction with Essence Scatter.

If your opponent casts Murder, then yes, you can cast Fling in response. When your opponent casts Murder, it goes on the stack, and you then have a chance to respond to it before it resolves.

You respond with Fling, which requires you to sacrifice a creature as part of casting it. Now the stack is Fling on top, with Murder below it. If no one else has any response, then Fling will resolve, dealing damage.

Then murder will attempt to resolve, but as it no longer has any legal targets (because the creature it was targeting no longer exists), it will fail to resolve and just go to the graveyard instead.

608.2b If the spell or ability specifies targets, it checks whether the targets are still legal. A target that’s no longer in the zone it was in when it was targeted is illegal. [...] If all its targets, for every instance of the word “target,” are now illegal, the spell or ability doesn’t resolve. It’s removed from the stack and, if it’s a spell, put into its owner’s graveyard.

Note that even if your opponent wanted to cast Murder in response to you casting fling; they couldn't target the creature you sacrificed because it was already sacrificed as part of casting Fling.

However, Essence Scatter cannot do anything to a creature on the battlefield; it only targets creature spells. A spell only exists on the stack; when you have declared that you are casting a creature, but before that creature has resolved. If your opponent casts a counterspell like Essence Scatter, you cannot do anything with Fling and the creature you are casting. Fling requires you to sacrifice a creature, which means a creature permanent on the battlefield. You cannot sacrifice a creature spell.

109.2. If a spell or ability uses a description of an object that includes a card type or subtype, but doesn’t include the word “card,” “spell,” “source,” or “scheme,” it means a permanent of that card type or subtype on the battlefield.

and

111.1. A spell is a card on the stack.