Okay Shikigami Manipulation gives my improvised weapon a +1 for every 4 caster levels the magic item has. So If I've got a book of lesser extend summoning, CL: 17, I'd have a +4 book.
Extemporanous Channeler then gives me the ability to spend one point of generic focus to give my improvised weapon a +1 for every so many points I've got in my body still. So say I can give it a +2 so far. (Level 7)
Now I could make the weapon a +5, which is easy enough. But I've got another +1. Do I just lose it or can I make my weapons a +5 Flaming book?
Either way (Either with less enchantment or yes it does stack there) Can I then further enhance it with Legacy Weapon?
"The extemporaneous channeler can imbue the item with any one weapon special ability with an equivalent enhancement bonus less than or equal to her maximum bonus by reducing the granted enhancement bonus by the appropriate amount, such as reducing a +2 bonus to a +1 flaming enchantment. (...) This ability stacks with any other effect that grants an enhancement bonus to an improvised weapon, such as gloves of improvised might, to a maximum of +5."
The last part means it does stack with Shikigami Manipulation, up to the normal limit of +5. You can put one ability on it, reducing the bonus by the respective amount. In your case, you can either add a +1 bonus (for a total of +5) and a +1 special ability, or a +2 special ability (e.g. Holy) and keep the book at +4.