In the Advert for Arrow/Flash, Barry takes some time catching the arrow. If it was a bullet it would make more sense. But if you have seen the video you will see that Barry almost misses it and the arrow almost hits the target.
If this was to happen in the show shouldn't Barry catch it as soon as Olly release it?
Why is Barry so slow to catch it?
The reason the commercial spot was filmed that way was to increase the drama/excitement of the spot. The slow build-up of Oliver preparing to fire, and the flight of the arrow through the air, builds up a bit of tension, with the surprise catch at the last minute. That final shot (the thumbnail on the YouTube video) of Barry holding the arrow inches from his face is a pretty compelling image.
Since this was just a commercial, and not a full episode, we have no context for why Barry was interfering with Oliver's target practice, but the most likely explanation is exactly the one Oliver gives at the end:
Barry: "Woooah yeah!"
Oliver: "Show off"
The Flash, in the advert, appears to be coming from some distance away, so would be at a major disadvantage.
It's not unlikely this is the sole reason he almost misses the arrow.
Oliver Queens arrows move around 350ish FPS (assuming they are on the faster end of arrows.) this translate to about 240 mph. Barry seems to be moving about two-three times that speed. 240 times 2.5 is around 600 mph. Barry around at the start of season 1 is has a top speed around 750ish. He breaks mach 1.1 by episode 6 and at the end of season 1 he is a mach 2. And because this clip was released near the beginning of season 1, 600 mph would be pretty close. If you do the math assuming he could run around 23 mph without super speed and with it he runs at 700 mph he is around 30 times faster than a regular human. Finally to answer your question why did it take him so long to catch the arrow: if you watch the clip in slow mo you can see right when the arrow is being released the flash came out over the hill around the same distance from the arrow as the arrow was from the target. That means if he were to pass up the arrow exactly when the arrow hit the target he would be moving at twice the arrows speed. He actually passes up the arrow when the arrow is halfway to the target. the only problem is that he then has to go in front of the arrow and gain enough distance where he could turn around in time/ catch the arrow without being hit and he cant just turn around at full speed he has to slow down and stop so the would take even more distance thus by the time he could do all that the arrow would be near the target. Finally this is all assuming the barry is traveling at full speed. He might be traveling at 2/3rd of his full speed. It like you/me running pretty fast at 15mph 4 min mile pace and we could still travel faster but we would rather not.
He's not "slow to catch it". He got there as fast as he can. He can't instantaneously teleport.
