When and how should I use Restoration Angel in the Avacyn's Glory deck? I understand Flash means it can be used any time like an Instant. What is the purpose or situation for exiling a non-angel I control then regaining control?
Many cards have an ability that triggers when coming into play. With Restoration Angel, you could re-trigger one such ability.
For the deck you mentioned, Goldnight Commander has the following ability:
Whenever another creature enters the battlefield under your control, creatures you control get +1/+1 until end of turn
So, when you play Restoration Angel and remove any other creature, your creatures get +2/+2 instead of just +1/+1. If that other creature is Geist-Honored Monk then the boost to all creatures becomes +4/+4.
Alternatively, you can dodge spells and abilities this way. If a non-angel you have is targeted by a spell or ability (say Shock) then removing the target from play temporarily will cause that spell/ability to miss and do nothing instead. As @skovacs mentioned in the comments, this can also apply to unwanted enchantments on your non-angel creatures.