Can a character that does not kneel to attack make two attacks in one challenge phase?

For Example, can a character with two icons(military and power) that is not required to kneel to attack able to make a military then a power challenge in the same phase?

Sure.

The only requirements when you declare attacker (or defenders for that matter) are that they have the appropriate icon and are standing when they are declared. If the meet those requirements for every challenge, they're good to go. Nothing limits characters to one attack per round.