Assumes that you advance at level 10; if not, add 6 leftover SP.

Level 10: +1 Magic Claw (1)
Level 11: +3 Improving Max MP Increase (3)
Level 12: +3 Improving Max MP Increase (6)
Level 13: +3 Improving Max MP Increase (9)
Level 14: +1 Improving Max MP Increase (MAX), +1 Fire Sprite (1), +1 Magic Claw (2)
Level 15: +3 Magic Claw (5)
Level 16: +3 Magic Claw (8)
Level 17: +3 Magic Claw (11)
Level 18: +3 Magic Claw (14)
Level 19: +3 Magic Claw (17)
Level 20: +3 Magic Claw (MAX)
Level 21: +3 Fire Sprite (4)
Level 22: +3 Fire Sprite (7)
Level 23: +3 Fire Sprite (10)
Level 24: +3 Fire Sprite (13)
Level 25: +3 Fire Sprite (16)
Level 26: +3 Fire Sprite (19)
Level 27: +1 Fire Sprite (MAX), +2 Magic Guard (2)
Level 28: +3 Magic Guard (5)
Level 29: +3 Magic Guard (8)
Level 30: +2 Magic Guard (10), 1 Leftover SP

Summary:

MAX Magic Claw
MAX Fire Sprite
MAX Improving Max MP Increase
MAX Magic Guard
0 Magic Armor
1 Leftover SP

Explanation:

1 SP goes into Claw at level 10 so that you don't have to go through the hell build with MP Increase, which is maxed first in order to get as much MP possible. 1 SP into Fire Sprite for fun, extra damage, and the Defense bonuses, then max Claw. Max Sprite next for even more damage, then max Guard last (since monsters shouldn't be able to 1HKO you at 2x anyway). The leftover SP go into

Level 30: +1 Teleport (1)
Level 31: +3 Fire Pillar (3)
Level 32: +3 Fire Pillar (6)
Level 33: +3 Fire Pillar (9)
Level 34: +3 Fire Pillar (12)
Level 35: +3 Fire Pillar (15)
Level 36: +3 Fire Pillar (18)
Level 37: +2 Fire Pillar (MAX), +1 Magic Booster (1)
Level 38: +3 Magic Booster (4)
Level 39: +3 Magic Booster (7)
Level 40: +3 Magic Booster (10)
Level 41: +1 Magic Booster (11), +2 Meditation (2)
Level 42: +3 Meditation (5)
Level 43: +3 Meditation (8)
Level 44: +3 Meditation (11)
Level 45: +3 Meditation (14)
Level 46: +3 Meditation (17)
Level 47: +3 Meditation (MAX)
Level 48: +3 Elemental Reset (3)
Level 49: +3 Elemental Reset (6)
Level 50: +3 Elemental Reset (9)
Level 51: +3 Elemental Reset (12)
Level 52: +3 Elemental Reset (15)
Level 53: +3 Elemental Reset (18)
Level 54: +3 Elemental Reset (MAX)
Level 55: +3 Teleport (4)
Level 56: +3 Teleport (7)
Level 57: +3 Teleport (10)
Level 58: +3 Teleport (13)
Level 59: +3 Teleport (16)
Level 60: +3 Teleport (19)
Level 61: +1 Teleport (MAX)
Level 62: +3 Slow (3)
Level 63: +3 Slow (6)
Level 64: +3 Slow (9)
Level 65: +3 Slow (12)
Level 66: +3 Slow (15)
Level 67: +3 Slow (18)
Level 68: +2 Slow (MAX), +1 leftover SP (1)
Level 69: +3 leftover SP (4)
Level 70: +3 leftover SP (7)

Summary:

MAX Fire Pillar
MAX Meditation
MAX Elemental Reset
MAX Teleport
MAX Slow
11 Spell Booster
0 Fire Arrow
7 Leftover SP

Explanation:

According to SP, Fire Arrow's max level is 20 for Flame Wizards (90 attack, 40% mastery), and Fire Pillar's max level is also 20 (100 attack, 60% mastery, hits 6). Thus, Fire Pillar is naturally the better choice, and is maxed over Fire Arrow.

11 Spell Booster comes right after Fire Pillar just to speed it up some, and 20 Meditation after that in order to power it up. If you prefer power over speed, swap the order of Booster and Medi.

Since I'm not quite sure what Reset does (and Google's translation was crap), I just placed it next. I'm assuming it either negates resistance to fire or reduces elemental damage that you take. Teleport comes next, then max Slow (which I'm guessing would be as useful in conjunction with Fire Curtain as it is with Mist). The last 7 SP can then be used on Magic Armor, Fire Arrow, or Spell Booster.

Note: Ifrit and Meteor are apparently unavailable until level 100.

Level 70: +1 Fire Curtain (1)
Level 71: +3 Fire Curtain (4)
Level 72: +3 Fire Curtain (7)
Level 73: +3 Fire Curtain (10)
Level 74: +3 Fire Curtain (13)
Level 75: +3 Fire Curtain (16)
Level 76: +3 Fire Curtain (19)
Level 77: +3 Fire Curtain (22)
Level 78: +3 Fire Curtain (25)
Level 79: +3 Fire Curtain (28)
Level 80: +1 Fire Strike (1), +2 Elemental Amplification (2)
Level 81: +3 Elemental Amplification (5)
Level 82: +3 Elemental Amplification (8)
Level 83: +3 Elemental Amplification (11)
Level 84: +3 Elemental Amplification (14)
Level 85: +3 Elemental Amplification (17)
Level 86: +3 Elemental Amplification (20)
Level 87: +3 Elemental Amplification (23)
Level 88: +3 Elemental Amplification (26)
Level 89: +3 Elemental Amplification (29)
Level 90: +1 Elemental Amplification (MAX)
Level 91: +1 Partial Resistance (1), +1 Seal (1), +1 Saved SP (1)
Level 92: +3 Saved SP (4)
Level 93: +3 Saved SP (7)
Level 94: +3 Saved SP (10)
Level 95: +3 Saved SP (13)
Level 96: +3 Saved SP (16)
Level 97: +3 Saved SP (19)
Level 98: +3 Saved SP (22)
Level 99: +3 Saved SP (25)
Level 100: +20 Meteor Shower (MAX), +8 Ifrit (8)
Level 101: +3 Ifrit (11)
Level 102: +3 Ifrit (14)
Level 103: +3 Ifrit (17)
Level 104: +3 Ifrit (MAX)
Level 105: +3 Fire Strike (4)
Level 106: +3 Fire Strike (7)
Level 107: +3 Fire Strike (10)
Level 108: +3 Fire Strike (13)
Level 109: +3 Fire Strike (16)
Level 110: +3 Fire Strike (19)
Level 111: +3 Fire Strike (MAX)
Level 112: +3 Seal (4)
Level 113: +3 Seal (7)
Level 114: +3 Seal (10)
Level 115: +3 Seal (13)
Level 116: +3 Seal (16)
Level 117: +3 Seal (19)
Level 118: +3 Seal (MAX)
Level 119: +3 Partial Resistance (4)
Level 120: +3 Partial Resistance (7)

Summary:

MAX Fire Curtain
MAX Fire Strike
MAX Elemental Amplification
MAX Meteor Shower
MAX Ifrit
MAX Seal
7 Partial Resistance
0 Leftover SP

Explanation:

Fire Curtain is maxed first, and would be used in training instead of Poison Mist. 1 Fire Strike is added for fun, and to clean up after Curtain on flat maps. Amp is added next in preparation for Meteor. 1 Partial Resistance increases your resistance to fire by 21%, and 1 Seal can be used if magic attacks are giving you trouble.

At this point, you should start saving your SP for Meteor and Ifrit. Once you obtain them at level 100, max Meteor, then dump the remaining points into Ifrit and start maxing it (it replaces Fire Sprite). After that, you can max whatever you want; I recommend you max Fire Strike and Seal, then dump the remaining points into Resistance.

Note that if you want to build your Wizard as if it were an Explosion-first F/P, switch Fire Strike with Fire Curtain.