Im wondering if I can deploy with a combat shotgun and a hades assault flamer?

RAW it is no problem at all, as long as you are within the Max. Carrying Weight.

How ever the book also says that the best way to determine how much you can carry, is to use common sense. As a guide the book suggest one basic/heavy + ammo and one or two pistol and/or melee weapons.
But if you and your GM feels comfortable with you carrying both the flamer with its fuel cannisters strapped to your back and the shotgun + ammo, along with all of your other gear, then go ahead.

And if you meant to ask whether you could somehow start with them as part of your gear, then the answer is also yes, either clearly within RAW, or by stretching RAW:
You can have a regiment with the combat shotgun as Main Weapon and the assault flamer as a favoured basic weapon, then start as a Weapon Specialist, hey presto.
Or you can add one of them to the Regimental Standard Kit by paying the points, so that everyone has it and take the other through the class or Main Weapon again.

I allow the Armsman talent to allow a character to carry more than the basic weapon + 2 sidearms limits (since it's not actuaally him carrying it).

That's not strictly RAW, though. RAW says that "anything sensible" goes. A lasgun and an autogun f.ex. would totally be doable for a strong~ish character: I've seen people carry two such longarms without issue and I think that's what the game is trying to emulate. Three, four or more longarms is going to be a problem though as you run out of places to put them...

That awkward moment when you click on a link to see if there is a potential homebrew rule for your regiment's favoured weapon... and then see one of your players asking about his PC's set up.

:-D