So for much of their history the Outworld's Alliance Mech units were asssigned to their Air wings.
From field Manual Periphery- The grenadiers are part of the 5th air wing's Joyless Rodgers. The flag of the air wing is a frowning skull on black with shattered crossbones.
From Camospecs-
https://camospecs.com/unit/5th-alliance-air-wing/The 5th AAW uses a combination of black, grey, blue-grey or silver creating bands on the aft half of fighters with black vertical stabilizers. Forward section color is dependent on the Regiment but uses one of the four colors. Squadrons use a highlight color to trim stabilizers and leading edges.
It does note that the commander of the air wing is eccentric and dresses in an age of sail uniform. So you might look to naval uniforms of the 18th and 19th centuries for inspiration on scheme beyond the colors and aerospace examples.
Individual battallion insignias are described on Sarna. The only colors mentioned are white and gold in the command battallion insignia- which is the only mech battallion as of 3064.
As of 3064 they are a combined arms regiment, 1 of mechs, 1 jump infantry, one other infantry.
It is unclear if the batallions remain combined arms in FM: 3145 but they have been detatched from the 5th air wing as part of the Raven Alliance.