I'm not going to do on a 5 second basis, I'm going to do a one cast on all skills basis over 3 seconds. In a 1v1 situation, no minions, no alt targets, no bounces, with a 1.0 AS, no item activation or any MR

Ahri; Q: 946 W: 1,080 E: 530 R: 4,635 Total: 7,191 Damage

Akali; Q: 1,090 (AA) E: 230 R: 2,250 Total: 3,570 Damage

Alistar: Q: 750 W: 975 Passive: 125 Total: 1,850

Amumu: Q: 1,020 W: 72 + 38.1% of their max health E: 675 R: 1,150 Total: 2,917 + 38.1% max health

Anivia: Q: 680 E: 1,350 R: 1,230 Total: 3,260

Annie: Q: 945 W: 1,030 R: 1,855 Total: 3,830

Blitz: Q: 1,300 R: 1,500 Total: 2,800

Brand: Q: 890 W: 855 E: 760 R: 850 Total: 3,355

Cass: Q: 1,035 W: 645 E: 740x6 R: 1,050 Total: 7,170

Cho: Q: 1,305 W: 975 E: 380x3 R: 1,350 Total: 4,770

Diana: Passive: 890 Q: 930 W: 828 R: 1,640 Total: 4,288

Fiddle: W: 630 E: 595 R: 2,325 Total: 3,550

Fizz: Q: 730 W: 420 E: 1,020 R: 1,450 Total: 3,620

Gragas: Q: 1,185 E: 740 R: 1,450 Total: 3,375

Heimer: Q: 3,144 W: 835 E: 900 Total: 4,879

Karma: Q: 870 W: 1,005 E: 1,080 Total: 2,955

Karthus: Q: 1,260 E: 1,080 R: 1,150 Total: 3,490

Katarina: Q: 650 W: 450 E: 560 R: 2,350 Total: 4,010

Kennen: Q: 985 W: 735 E: 845 R: 750 Total: 3,315

Lux: Q 960 E: 840 R: 1,250 Total: 3,050

LeBlanc: Q: 1,230 W: 845 E: 640 R: 1,722 Total: 4,437

Morgana: Q: 1,200 W: 855 R: 2,050 Total: 4,105

Nunu: E: 1,275 R: 3,625 Total: 4,900

Orianna: Passive: 720 Q: 680 W: 950 E: 480 R: 1,000 Total: 3,830

Shaco: W: 295 E: 1,210 R: 1,600 Total: 3,105

Swain: Q: 1,155 W: 940 E: 1,035 R: 870 Total: 3,700

Syndra: Q: 955 W: 940 E: 650 R: (2 extra spheres) 2,280 Total: 4,825

Teemo: Q: 1,060 E: 1,740 R: 1,400 Total: 4,200

Veigar: Q: 860 W: 1,320 R: 2,500 Total: 4,680 (against someone with 1,000 AP)

Viktor: Q: 910 E: 950 R: 1,455 Total: 3,315

Ziggs: Passive: 489 Q: 905 W: 560 E: 2,200 R: 1,400 Total: 4,294

Zyra: Q: 830 W: 334 E: 700 R: 1,100 Total: 2,964

There, mainly all the AP Champs that get played as AP champs.

Highest AP burst over 3 seconds is Ahri and Cass, but the situation you presented will never happen.

However, ACTUAL burst is less then 2 seconds, which in that case, the title goes to Veigar, his W+E+Q+R combo will hit in less then a second if planned o0t properly.

For those who say my calculations on Veigar's ultimate is wrong; 500 + 120% Of his AP + 80% of enemies AP = 500 + 1,200 + 800 = 2,500

This is a ONE VS ONE SITUATION, Fiddle's crows can't bounce. Swain's ultimate, releases 1 crow per enemy up to 3, each crow can only hit one target, stuff like that.