if a character like Kyle Rayner of Fatality, gains the power to use a certain team ability (quintessence and Mystics in this case), can they use that team ability even if they're the only characters to be able to?

I know that for characters to use a team ability there must be at least two of them in the map, so I'm asking if they're power is an exception

Yes, they can.

And you're wrong here. Every character that has a TA can use that TA regardless of who else in their force.

To clarify, some TAs in their specific descriptions say they interact with other TA-using characters. For example:

BATMAN ENEMY: Characters using the Batman Enemy team ability may replace their attack value with the unmodified attack value of an adjacent friendly character using the Batman Enemy team ability.

This TA only works if there is at least one other Batman Enemy on your team since your character needs to be adjacent to another character using the TA.

But many other TAs work completely and totally fine on their own. For example:

HYDRA: When this character is adjacent to a friendly character making a ranged combat attack, modify the target’s defense value by -1 if the target is within line of fire of this character.

This requires no other HYDRA characters. Any adjacent friendly character, regardless of TA, can take advantage of this TA.

Some TAs don't need any other characters, period. They will work in a complete vacuum. For example:

AVENGERS INITIATIVE: Characters using the Avengers Initiative team ability treat hindering terrain as clear terrain for movement and line of fire purposes.

You don't need any other characters at all; this would work fine even if your force consisted of just a single character.



In other words, nothing in the general rules for TAs require you to have specific numbers of characters. Some TAs will tell you they need other characters to work, but that's specific for that particular TA and not *ALL* TAs.

To clarify the clarification...

Even when you are dealing with one of the TAs whose functionality require two or more people to make use of the team ability, you are not required to have multiple characters with that symbol. You could use a wild card or something.

I think OP is confusing TAs with ATAs. To have an ATA, you need to start with a theme team (at least 2 figures with a matching keyword).
That has nothing to do with the TAs on the figure's dial or that they can use through a power/trait/whatever.