Since you already paid for purple and are looking for ways to make it work, I will respect that. From a having-fun-perspective that’s totally fine and I will try to help you out a little bit.
@Janejana already mentioned some important things. I will try to go a little deeper since my stakeholder meeting today got canceled and I’m in a mood to talk your ears off.
So prepare for a wall of text. 
You are going URAD which is a very good damage anointment but it forces you to give up healthgate, meaning you need ways to survive enough punishment while dealing damage fast to kill your enemies.
For URAD, there are two routes to go down on Fl4k:
1.) Shield + Deathless artifact
That‘s your way and you pair the Deathless with an Atom Balm prefix which helps your multi target damage from URAD explosions. That’s totally fine.
And you chose to take a more tanky shield with the Transformer as that takes out an entire element out of the equation which is dangerous to your shield, good. Additionally, it has absorb parts which also help you with defense.
It’s a viable way and provides survivability. But since you’re going purple you could either chose a shield that helps your pet do damage (via Take this skill) like the Faulty Star or you could add some damage to you by going radiation Old God (DLC2). That will buff your URAD damage which applies to all your damage dealt. So even slams, melee etc. The Old God can also have 3 parts on it unlike most other shields and those can also be absorb. It’s good on offense and defense.
2.) The other option you could chose for keeping URAD up is: Front Loader and an artifact.
The Front Loader shield is the tool here, it doesn’t provide a lot of offensively but it ensures that URAD is always-on.
But the shield allows you to pick up an artifact that boosts your damage: The Pearl of Ineffable Knowledge (Quest reward, DLC2). This artifact stacks by dealing damage to your enemies and after 15 stacks you get 90% gun damage and another 1.16 multiplier to your damage. So, it is very powerful, easy to stack and it covers the damage gap you created by going purple a bit.
Passive rolls on artifacts:
The Pearl has a limited pool of passives, try to find one with mag size and fire rate.
If you want to keep your Atom Balm Deathless, try go get one with gun type damage (of the weapon type you are mostly using. In the video I see you mainly running the Reflux, which is fine) so go for shotgun damage. This weapon type damage is a powerful v2 damage multiplier and will help you out noticibly.
Pair that with either radiation damage (which can roll twice for double the value) and/or mag size, fire rate, reload speed or AOE damage (some of your weapons and URAD explosions benefit from it, not the Reflux though).
My recommendation: Front Loader + Pearl as that will net you more consistent damage for bossing and mobbing. URAD explosions won’t happen too too much during a boss fight.
The anointment on the shield should be 50% elemental damage on action skill end like you have. You could either try to find several of the shields of your choosing with various elemental anoints to match elemental resistances or settle for cryo as that has no penalty against flesh and covers your armor damage needs; shields are covered by URAD. But don’t stack two of the same elemental anoints on shield and grenade as they will not stack. So go one cryo, one fire for example.
Class Mod:
You have the Bounty-Hunter which is a great COM as it lets you go from mobbing to bossing without worrying. The red text makes it so that you get the armor damage bonus from Hunter’s Eye against all bosses against all of their health bars (shield, flesh, armor). This bonus is also v2, so again, powerful.
Another thing the red text effect does: it allows you to stack your specced Hunt skills by dealing gun damage. So even without kills you can stack Interplanetary Stalker, Second Intention and The Most Dangerous Game (if you damage a Badass) which is especially nice when bossing.
Try to get one with +3 in Most Dangerous Game as that will give you some nice gun damage (and other perks) and +2 in Frenzy/Hunter’s Eye.
The Stalker COM is even more powerful – for mobbing that is. Like @Janejana already said: The 25% Hunt skill power stacks with Big Game. When using a COM with +3 in Big Game you gain 85% Hunt skill power. So Interplanetary Stalker, Hunter’s Eye (yes, it’s a Hunt skill!), Frenzy, Second Intention, Furious Attack, Most Dangerous Game almost get doubled. You see where this is going.
Passives on COM:
Again, try to get Weapon Type Damage for the weapon you’re using the most. Same goes for manufacturer crit damage as that multiplies your crit damage, Weapon Crit, Weapon Damage, Reload Speed, Magazine Size are all good choices.
Grenade:
Since most of the grenades in this game are not good at killing things, you can consider them tools. The undisputed best tool in this slot for Fl4k is the Hunter-Seeker grenade. It got buffed recently and does nice damage. Also, it shoots out bullets which do not benefit from your gun damage bonuses but from your damage bonuses and, more importantly, they can trigger anything gun related and even crit related as they can naturally and Megavore crit.
So they trigger Head Count, Leave no Trace, Furious Attack and when paired with the Bounty-Hunter they even stack your Hunt skills for you (e.g. IPS). As a plus: When running the War Loader he throws it as well and it gets the pet mayhem scaling (x 51) multiplier and it destroys.
When you’re going with a cryo ASE on your shield, you could take the 25% on grenade thrown anoint on the Hunter-Seeker. You are independent of your action skill use with this anoint and the damage is also v2 which is great.
Try to find a Mitosis Hunter-Seeker as that will increase the grenade count. So more bullets shot at the enemy. It will perform better.
Weapons:
Pick whatever powerful weapon you like as long as it has the URAD anoint on it.
Reflux is great (Armor, flesh, shield is covered). The Hellwalker is really strong even though it is fire-locked. It just does so much damage. At the end of this post I will link a guide for you. There’s more for you to read on weapons. Knock yourself out with it.
Pet:
As @Janejana already said: You are going elemental weapons and have URAD anoint. The Skags do give you gun damage (and damage/fire rate) but only a tiny bit when not buffed by Barbaric Yawp. Whereas the Scorcher buffs your elemental damage and adds another multiplier to your damage that will most likely surpass the bonuses from the Skags. Even though the health regen will go to waste when going Deathless; it will help out a bit when going Front Loader as that shield keeps 40% of your health intact. The damage part is more important here.
Skills:
In any case, take one point in He Bites as that will help your pet stack Frenzy which is a powerful v1 damage bonus. Regular attacks, especially on the Scorcher, will not consistently stack and maintain Frenzy. This one point helps tremendously; even if you need to take if from Frenzy itself. (Plus if you find a Bounty Hunter with + Frenzy, that’s covered as well.)
While keeping your purple parts (that doesn’t sound right ) and action skill I took the freedom to change your spec like this:
I hope this helps.
Also, check this community resource run by people way more familiar with Fl4k that I am:
