I made a topic about this a long time ago.
Give this a read and see if it helps.
Sorry for late reply. Tested these Attack animations for several days. (Testing was done on the PSX pal english version)
0xFE - Braver limit animation from magic menu (Cloud's limits)
0xC8 - Braver limit animation from E.Skill menu (0xFE - 0x36 = 0xC8)
0xD0 - Grenade Bomb limit animation from E.Skill menu (Barret's limits)
0xD7 - Seal Evil limit animation from E.Skill menu (Aeris limits)
0xFD - Gauntlet limit animation from E.Skill menu (Yuffie's limits)
0xFF - All Creation limit from E.Skill menu; (no animation)
0xD5 - All Creation limit animation from manipulated enemy menu; (animation displayed)
0xDD - Beast Flare limit animation from manipulated enemy menu; (animation displayed)
Beast Flare animation value from magic menu: 0xDD + 0x60 = 0x13D (we can use only 1 byte)
Beast Flare animation value from E.Skill menu: 0x13D - 0x36 = 0x107
Beast Flare animation value from manipulated enemy menu: 0x13D - 0x60 = 0xDD
It seems, that Summon menu can use only Summons animations.
So, the sequence of animations, on the PSX version, is as follows:
000-035: 54 Magics
036-04D: 24 E.Skills
04E-05F: 18 Summons
060-FD: 158 Enemy magic attacks (not sure about 158)
0FE-143: 70 Limits?
144-14A: 7 Toy Box animations, or 0xE4-0xEA: if used from enemy attacks
14E-15D: Enemy throws Cloud's weapons, or 0xEE-0xFD: if used from enemy attacks
0x14E (or 0xEE from enemy attack) crashes game, suppose to throw Buster Sword, but it seems that there is no throw animation for Buster Sword
0x14F or 0xEF from enemy attack: throws Mythril Saber.
I saw in the PSX code that FF7 adds 0x48 to the Attack Id if we use E.Skills. May be there is also code that adds to Animation Id.
Give this a read and see if it helps.
Thanks, it helped.
Edit: Found one way to display Beast Flare animation from magic menu.
There are current attack values in battle:
Beast Flare attack used from AI script; Attack 1 values: 02 01 3F
14 00 41 71 00 83 00 02 00; Attack 2 values: FF 05 00 00 00 00 00 00 FF FF 03 00
Beast Flare attack used from magic menu; Attack 1 values: 02 01 3F
02 00 41 71 00 83 00 02 00; Attack 2 values: 02 01 00 00 00 2E 00 00 FF FF 03 00
(Attack 2 values used with: Satan Slam, Finishing Touch and may be with Blade Beam)
If this "02" byte is changed to 14 in a debugger while the value is set in it, then Beast Flare animation is displayed from magic menu.
In the battle, there are also values in which menu the character is in. When character points on enemies with Beast Flare attack from magic menu, these values become: 02 01 71.
Where 02 - Command Id, 01 - Menu Id, 71 - Attack Id. If 02 byte changed to 14 (Limit Command Id), then Beast Flare animation is displayed from magic menu. This works for all Vincent's second limit attacks, even with Satan Slam attack, two animations are displayed properly from magic menu.