Is there any greater IV than 90% of Magikarp?
My trainer level is 26 and I have caught 217 Magikarps in total of which the best IV is 13-13-14 of 88.9%. Should I evolve him or there are still some better IVs? I am tired of catching Magikarps now. I have two pokemons of 100% IV(Exeggutor and Rattata). I think I should focus on the pokemons of greater than 97% IV in future. How do you think?

Answers
You should rename it to "MyCurrentlyBestMagikarp" or "BestMagikarpIFoundYet", since there are much better ones in the pond. I'd recommend to save your candies till you catch a better one (100% 15/15/15 Magikarps do exist, I recently found one. Of course it became a Gyarados with Bite/Crunch, but still..)
From my experience 91% are not that uncommon. May have to collect enough candies to evolve 2 by the time you find one though and then you can evolve both and pick the best movesset to power up. The best I have found is 96 and it got twister which I'm happy is no longer available. My luck with movesets for 93% have been pretty good though. Bite/hydro pump and dragon tail/crunch. 93% + are very hard to come by...
The odds of a perfect IV Pokémon are 1:4096. The odds of a 44/45 Pokémon are 1:1024. These are incredibly high standards, particularly when you add in the risk of the move set evolution.
For Pokémon like Gyarados or Dragonite where every CP matters, I set a minimum of 42 (Gyarados) or 40 (Dragonite) for evolution. For small fry, like Natu, the bar is much lower.
I evolved a 96% and 91% gyarados that both got the dreaded Twister move. ? I have a 93% lined up to evolve after water event. Plus I was lucky enough to catch a 73% wild gary. I am happy with all my Gyarados despite being less than perfect IV. There are other Mon though that I am convinced my biome doesn't produce Amazing (Valor) IVs. Like Tediursa right now. I can evolve 3 but waiting on a higher IV mon that doesn't ever come my way. Maybe you've got a similar situation with your magikarp.
No, don't bother with setting such a high bar. I'd personally say 82 (whenever the trainer gives you the highest appraisal) is good, however, this is given that if the magikarp is at least Level 28, so you have to spend minimal stardust (19000 or less) to take it to level 30.
Otherwise, I would only evolve karps that are 91+, but even then, I'm much more of an advocate of evolving a high level karp over a high IV one (unless the IV is unacceptably poor, say below 67). I have a 87 IV one waiting for me to evolve, already at level 30.
If you want true gym placement, you wouldn't go for a gyarados anyway. I learnt this the hard way by maxing out my 100 IV and still not getting superb placement. You should really be aiming Snorlax/Dragonite/Tyranitar for the gym placement.
My 6 Gyarados are at 100, 91, 89, 89, 87 and 93. (The 93 one has twister).
Actually Gyarados is great for gym placement and way more common than snorlax, dragonite, Blissey or tyranitar. Try to break the psychological barrier of level 30 with a couple of your Gyarados and see the results. I think Gyarados is one of the few Pokemon that is worth to power up above 30. Specially the new versions with dragon tail/anything. They are great defenders
Before this event, i had less than 100 candies and wondered if I would ever get a Gyarados. After the event I ended up with about 500 candies, so I evolved my best magikarp from the event: level 28 78% IV. No regrets. Plus, it got DT/OR. I powered it up and is my highest CP mom now. I could have waited for a bigger one, but I wouldn't have enjoyed that too much. I'm all for grinding but I need some fulfillment in this game too! Finally getting that Gary after 9 months was totally worth it!
Of course. For every Pokemon the highest possible IVs are 100%. I've caught wild magikarp at 91 and 93% IV. I also hatched several 96 and 98% when they were included in the egg pool.
To answer your question. I wouldn't evolve your current best one because it is too low level (IVs are OK, but is not worth it to spend dust and so many candy to take it to a decent level). But if you really want to have your first gyarados go ahead and start hunting for a better one in a near future.
Once you are level 30 you may encounter level 30 magikarps that are worth to evolve even being only 82% IV (I got a few of them). That way you get a big fish to place on gyms straightaway, with no investment of dust