Nice guide! As the creator of the first hybrid Rook guide, I can say that this build is fully playable with the amulet of teleportation.
The teleport amulet is friggin amazing on Rook. I use it as a "rejuvenation potion" to teleport back to my crystal. This solves most of my early game mana issues. It halves your shopping time and allows you to easily gank. Sure, BotF will give you more lane control, but with the teleport ammy I can run my HP into the ground and then teleport back to heal. Also, there are several DGs that are excellent counters to Rook, such as Reg. If Reg is in my lane, I'll just teleport to the other side where I can maintain an advantage.
If I may make a suggestion, I would recommend adding the Orb of Defiance to your build. You don't need to conserve consumable slots since you have the tele ammy, and it hilarious using it inside your tower farm as you're about to die. With the low amount of health in this build, it helps your HP and armor quite a bit. I've had games where I will activate it when I'm at low HP, and my entire team will teleport over to my tower for a gank. I would substitute it for Narmoth's Ring.
Also, I'd suggest perhaps switching Trebuchet for Tower III. The trade-off is 6 towers at level 7 instead of 6 towers at level 13. I sort of think they are more scary at level 7, personally. Also, it allows you to throw up 3 towers on each side of the map, instead of 2.
I'm partial to God Strength, but usually I will only get it after level 10 (see my guide for more info).
EDIT: Combat mana potions only cost 200????? WTF? Thx for the info.
Maybe i would use Blade of the Serpent instead of Amulet of Teleportation.
BotS is the friggin worst favor item for Rook. If you want a mana favor item, use CoPM (on Leviathan) or EoM. EoM gives Rook freaky levels of mana early game.