When should I watch The New Captain, Shusuke Amagai Arc?

I haven't seen past there yet but from my understanding the next arc after that continues on from after Ichigo's fight with Grimmjow in Las Noches as indicated by wikipedia

The episodes' plot continues to follow Ichigo Kurosaki's and his friends' battle against the Espada, the strongest of former Soul Reaper Captain Sōsuke Aizen's army, to rescue Orihime Inoue.

Source: Wikipedia - Bleach (Season 10)

also i do recall in the first episode of Season 9 the narration says the follow events occur before the sneak entry into Hueco Mundo. there is also some evidence to indicate that this is before then mainly that Chad and Rukia aren't thought to have been killed as it is implied near to the end of Season 9.

Ofcause being filler it's not canon and the contradicting evidence is with Chad and Uryu who were actually still training before the sneak entry yet they show to have their new powers which were only revealed after they entered Hueco Mundo (remember that Chad was being trained by Kisuke and Kisuke snuck Uryu out of the training room he was in when he expected Ichigo to defy the Soul Society and rescue Orihime)

Ignoring this contradiction one can assume that it takes place before Orihime was kidnapped but after Ichigo started training with the Visord (due to him being able to Hollowfy)