How would you guys handle a magic user taking the augment spell and using it to apply weapon qualities to their weapons. Some examples are things like Burn on an Axe (Flaming Axe), Blast on Arrows (Explosive Arrows), Ensnare on a Sword (Sword Whip). All of those would work fine narratively, and are in line with how the augment spell is described. However, I'm concerned that the attack spell would become far less desirable as the augment could be maintained and wouldn't require extra strain for each attack.

I think the player should still be able to do this sort of thing, but I'm having trouble figuring out how to properly balance it.

Any thoughts?

Because you have to burn a manoeuvre maintaining Augment, and burn an action just to cast the spell, the Attack option is always going to be alluring.

But for your question I would say yes, sure, that sounds fine, I would probably make it a Medium summon though and not just the basic spell

RB nailed it. Other things to consider:

The Flaming Sword can be disarmed.

The Flaming Sword guy's attacks are now probably going to be using the much scarier Magic Threat Table.