Why won’t the MK16 parachute deploy

You're right, that setup wont get you to Gilly and back, for a variety of reasons.

Here are four ways you can improve your game and make for yourself a rocket that will perform that mission. I'm assuming, since you're playing KSP in the first place, that you want the achievement of having made and flown the entire thing, not just downloaded someone's .craft file!

• Use Kerbal Engineer. It has no gameplay effects or flight computer, it just does a lot of calculations for you, including dV. Click here to get it from Kerbal Space Port.
• Do research and plan your missions. Real scientists do in-depth analyses to determine the dV needed to get to places, and you can to! Fortunately, the good folks at the Kerbal Space Program Wiki did most of that for you. Now, if only you had some sort of part that you could put on your ship to check that you have enough dV... cough cough.
• Watch tutorials. Everyone can brush up on their fundamentals and their advanced technique. A great place to start would be Scott Manley's tutorial series. Of all of the very best players, he has the most helpful and up-to-date tutorials, and ties in a ton of real-world rocket science that you might not have picked up on your own!
• Lastly, and most importantly, practice! You get better at games by playing them; even tough, physics-based games. Try new things. Maybe you need more fuel. Maybe you need a smaller payload. Maybe you need a different sort of staging or fuel arrangement. Personally, I'm a big fan of Asparagus staging for lifters and Caterpillar staging for transfer vehicles.

* Caterpillar Staging is when you have engines that aren't jettisoned with the fuel tanks, as pictured below. (The parts with the diagonal lines are meant to represent the 2m Rockomax decouplers.) Just like Asparagus Staging, Caterpillar Staging is meant to drop the dry weight of empty tanks and therefore keep the rest of the craft light and long range.

You're best bet is to err on the side of safety and use too many. The potential financial loss for chutes ($700 each for radial) is much less than the potential financial loss of your entire ship.

I'd love to be able to give you some simple formula like "Use 1 chute for ever x tons". But there is no simple formula. The complex formula can be calculated using the tool you've linked to.

That said, these are some excellent tips:

1. Balance your lander - position your chutes so you land as flat as possible.
2. Land on a flat surface - otherwise you could topple over.
3. Keep your ships flat - pancakes don't topple over.
4. Use modular girders or i-beams instead of lander legs. Modular girders and i-beams have 6x higher impact tolerance (80m/s) than the strongest lander legs (12m/s). You can land a 1000 ton ship on Kerbin with a single chute if it can survive a 80m/s landing.
5. Fire your rockets prior to landing to slow down your ship.

Good luck.