Know your route
Map knowledge is incredibly important in Shadowgun War Gamesm especially in Capture The Flag. The route you take to the enemy flag and back, and the routes your enemies will take, will be similar, and important to memorise.
It's okay if you're unfamiliar with the map at first, just spend the first round investigating all corridors, and getting a feel for your surroundings.
Just remember, the most efficient route isn't always the best one. Perhaps find a route which is out of the way, and using that to take the flag in a direction enemies won't expect - just remember they'll have their flag highlighted on their screens…
This is incredibly important in this game mode. If you actively intend to get flag captures, you will need to have a character with good speed and health.
As a result, Slade is a good early choice since he can regen health, but later on Jet is more efficient as he is much faster.
This is not to say other characters are not viable - you can easily play a support role. With the base characters, Revenant makes an excellent distraction to keep the enemy team busy, and Sara can heal allies, which is great if you stay near and support the flag carrier.
Once the enemy has the flag, you will have their location highlighted on your screen, so head right over to them. Finishing them off and collecting your flag should be your top priority.
This is where that map knowledge comes in - you should know roughly where the enemy will be moving from and towards, and using that information to cut them off.
On the reverse, if you have the flag, either take a smart route to your flag, or ensure you have a teammate supporting you, as getting into a confrontation with more than one enemy is unlikely to end well, regardless of your abilities.
Back 'em up
And this ties into our last point - if someone on your team has the flag, rush to back them up. Stay near them, shoot down enemies, and heal them if you can.
You might be disappointed about not getting the point for yourself, but if the carrier gets killed, you can always take the flag and continue on the mission, stealing all of the points for yourself - win-win.
You don't need many flag captures to win the game, only two, so work hard and you'll soon find victory. Just stick with your team.