With this gear you could defeat JK. You will both need to have 3 heal capsules, 3 fire capsules, 3 poison capsules, and 3 shock/curse capsules.
A tier will rarely drop 6 curse capsules so your better off 1 of you getting 3 shock, the other 3 curse.

Make sure to keep JK constantly poisoned/fire/shock/cursed. Block when he flashes red to attack. Block other jelly attacks and shield bounce for space. You will need to hit the blue blocks to clear the room as much as possible. When JK spins follow him and charge your weapon.

^^Do this to beat him. Expect to rez about 1-3 times each (at least). Expect to not beat him and be surprised if you do. The above advice is something that really needs to be coupled with personal experience vs him :(

Final Verdict: It is going to be very very tough and very very very not worth the energy it cost to beat him. You are better off taking the above advice and if you have 2 well-geared teammates, then fight him, if you don't then don't go to room 17. I know it's a crappy answer when you want to go beat him, but we have the best intentions when we suggest to not fight him yet :)

basically if you spend 3-4 rez's each (or more) you just wiped out your entire profit for the whole run. That's why we say skip him until you got 3-4* gear. Then you can die none to once, and not kill your profits.

http://wiki.spiralknights.com/Royal_Jelly

That’s a good read – covers how to deal with the Royal Jelly nicely.

“Handguns are not very effective because other jellies will often block your shot. Run up and hack away, ignoring the other jellies and pausing only to shield when the Royal Jelly spins. Use weapons or vials to keep the Royal Jelly poisoned, cursed, and on fire at all times.”

So, if you’re counting on using Shadowtech Alchemer for that purpose, it might backfire. I haven’t ever fought the Jelly King though – so I wouldn’t know. Also, Shadowtech Alchemer doesn’t inflict any status effects. And as the guide says, you might want to have something that can cause fire status. Maybe you could upgrade your brandish to Fireburst Brandish and keep using the Shadowtech. Or turn it into a Nightblade instead and get a Firotech Alchemer? I heard someone saying there are constructs there too, so the elemental damage could handy against them.

Another thing to note if you are going to rely on Shadowtech - your armor and helm ups only sword damage – not gun damage. Choosing Nightblade it will be good against Jellies and Gremlins – but not fiends and undead. With Fireburst, you’ll do good damage to Constructs and undead, but bad against beasts and gremlins. Your call, based on your preference.

As for your armors, I think they are fine. That is, if you plan on using your sword a lot. For jelly slaying, there are two adorable alternatives http://wiki.spiralknights.com/Chroma_Mask
http://wiki.spiralknights.com/Chroma_Suit

You can pick up one of them if you like – that way, both your gun and sword will do increased damage against jellies.

Edit: One of you might also want to consider getting a status inflicting bomb (at least 2-star) - perhaps poison or fire? Here's the list.. http://wiki.spiralknights.com/Bomb