Question: I've caught up with the Justice League and Justice League Unlimited TV Show. I intend to start watching the Justice League movies as well. 

What is the suggest viewing order for the [Justice League animated movies](http://en.wikipedia.org/wiki/DC_Universe_Animated_Original_Movies)?

Answer: 
The [same Wikipedia link](https://en.wikipedia.org/wiki/DC_Universe_Animated_Original_Movies#Continuities) that you mentioned also has the answer to this. Most of the films before the Justice League: The Flashpoint Paradox doesn't share any continuity. Only few do, which are: 

**Superman/Batman**
This continuity is based on the Superman/Batman story line.

* Superman/Batman: Public Enemies
* Superman/Batman: Apocalypse

**Justice League**
This continuity is based on the JLA (comic book) story lines published in 2000.

* Justice League: Crisis on Two Earths
* Justice League: Doom

**Batman: Dark Knight Universe**
This continuity is based on Frank Miller's Batman (Dark Knight Universe).

* Batman: The Dark Knight Returns – Part 1
* Batman: The Dark Knight Returns – Part 2

**Justice League: The Flashpoint Paradox** also works individually, but the ending set up a new universe similar to the comics. The film came after it severed the continuity and was called **DC Animated Movie Universe**:

This shared universe is based on The New 52 continuity.

* Justice League: The Flashpoint Paradox( End credit scene)
* Justice League: War
* Son of Batman
* Justice League: Throne of Atlantis
* Batman vs. Robin
* Batman: Bad Blood
* Justice League vs. Teen Titans
* Justice League Dark
* Teen Titans: The Judas Contract
* Suicide Squad: Hell to Pay (upcoming)

**Justice League: Gods and Monsters** This universe takes place in an alternate universe and has no connection to any of the other films

* Justice League: Gods and Monsters Chronicles (web series)
* Justice League: Gods and Monsters

Second season for Justice League: Gods and Monsters Chronicles was in works but shelved for now:

[![enter image description here](https://i.stack.imgur.com/IAfuY.png)](https://i.stack.imgur.com/IAfuY.png)

The rest of the films mentioned in that Wikipedia link are standalone and can be watched in any order.

As you might already know, there are [five Batman animated films](https://en.wikipedia.org/wiki/DC_animated_universe#Films) in the DCAU. But they sever the continuity to DCAU and the order of the rest of the DCAU [shared here](https://scifi.stackexchange.com/a/46692/6006).
**I personally would watch JLFP after Throne of Atlantis just so that it makes a little more sense (apart from the credit scene).** **IGNORE**

I have changed my mind. I have decided it makes more sense to watch JLFP before TOA as long as you believe that when Barry arrives into the new timeline it is after the events of JLW.

This design changes could be explained by the timeline changes. The different Flash suits make more sense (as he may have not made the New 52 Styled suit yet).
Batman's suit is teen to have a blue colour to it. In Batman: Bad Blood, his suit gets lighter and gains the blue colour, which could be more evidence.