Q: can I add two 14-50 outlets to one 50 amp breaker
I read a lot of NEC Article 210, and focused on 210.23. I see no restriction on outlet count. I have to conclude: you can have two or more outlets or receptacles on one 50 amp breaker.
Everything else about Harper's answer is great advice (although I personally think going above 1 inch conduit is a bit much). I would have just commented on his answer, but I'm not allowed to comment.
The section of the NEC he references doesn't restrict the number of outlets on a 50 amp breaker. If you interpret the permissible load as a restriction on outlets, then no circuit breaker in the house can have more than one outlet on it and you have to ignore that the section is exclusively about multiple-outlet circuits.
National Electrical Code 2014
ARTICLE 210 Branch Circuits
210.23 Permissible Loads, Multiple-Outlet Branch Circuits. In no case shall the load exceed the branch-circuit ampere rating. A branch circuit supplying two or more outlets or receptacles shall supply only the loads specified according to its size as specified in 210.23(A) through (D) and as summarized in 210.24 and Table 210.24.
This section is actually about multiple outlet circuits and the load they are allowed to carry. So a 50 amp branch circuit must only carry a 50 amp load. This is ensured with a 50 amp circuit breaker.
210.23(C) 40- and 5-Ampere Branch Circuits. A 40- or 50-ampere branch circuit shall be permitted to supply cooking appliances that are fastened in place in any occupancy. In other than dwelling units, such circuits shall be permitted to supply fixed lighting units with heavy-duty lampholders, infrared heating units, or other utilization equipment.
So immediately, this says nothing about restricting outlets. In fact, it's actually defining what "fixed" or "fastened in place" loads can be wired to a multiple-outlet (210.23) 50 amp circuit (210.23(C)).
Let's look at the referenced table too.
Nothing about only 1 receptacle. It references back to 210.23(C) for permissable load, but that's not a discussion of how many outlets can be on the circuit.
Here's how I think about it: An outlet is not a load. It is only the potential for a load. 210.23(C) discusses connected electrical devices (lights and stoves) that put an actual, defined load on the circuit. That's why it doesn't mention outlets.
The circuit breaker protects the wire, outlets, and a device plugged in from over drawing current, over heating, and starting a fire. If the circuit breaker protects at 50 amps, then the wire and outlet must be rated to handle 50 amps. If two 50 amp devices are plugged into two 50 amp outlets on the same 50 amp CB, and those devices actually draw full 50 amps (rare) or above 25 amps each, and they are used at the same time, the CB will trip. That's it's job, to protect the wires. And presumably the user won't plug too many devices in again.
This is the design of almost every circuit in your house. (There are exceptions for the small-appliance branch circuits, outlined in 210.11(C)) Multiple outlets are on almost every breaker. If you plug in a bunch of space heaters, you will trip the breaker, but the wiring will be protected.
Having said all that, check with your local inspector.
While I'm here, I might as well complete the answer... although Harper's answer perfectly covers everything else.
Q: using 6/3 wire in conduit
Don't use 6/3. You need THHN for conduit.
3/4 inch EMT conduit can take four #6 AWG wires. Code requires no more than 40% fill of EMT (NEC Chapter 9), so you can calculate this yourself. I haven't looked up PVC, but if you use 1 inch PVC, you'll be good and it will be a lot easier to pull.
Another tip: The ground wire is not considered current carrying and can be smaller. (2014 NEC, Table 250.122) For a 50 amp circuit, you can use a #10 AWG THHN copper wire. This will save some money and make pulling much easier.
Q: I have seen some wire nuts that can accept two 6 gauge wires but not three, which is what I will need.
Use terminals blocks or "polaris connectors." Search for polaris connectors online, and you'll get a lot of results.
Q: recommend PVC or liquid tight flex conduit
I would use EMT. I've seen PVC sag a little with time, so I think EMT looks better. Also, you might be able to use it as the ground return (although I would feel safer with a ground wire).
If it must be PVC or liquid-tight, I would go with PVC, but I haven't used either in a long time. Liquid-tight might be more expensive to get fittings for and it might be more difficult to install.