Strategies for playing The Masochist in Cosmic Encounter?
You should play as if you don't have an alien power, since Masochist's power is diametrically opposed to setting up 5 foreign colonies and it is extremely difficult to send all your ships to the warp. 

I will assume that you are playing with the latest edition of Cosmic Encounter by Fantasy Flight Games, because the Masochist is only available in this version. From the rule book, there are 72 total Cosmic Cards (82 with Flares). If you are playing a 5 player game, then there is just a 38% chance that one of the other 4 players does not have Mobius Tubes in their opening hand. You only have a 18% chance of having drawn a Card Zap to prevent Mobius Tubes in your opening hand. Even without a Mobius Tubes being drawn, you have several things working against you. 

The Regroup step isn't optional, so every turn you must return 1 ship to your colonies, which means that it would take a minimum of losing 7 Offensive Encounters (I will get to Defensive Encounters in a moment) instead of winning 5 Encounters. In general, your opponents should see you attempting this strategy long before you can actually win with it. They will avoid allowing you to lose ships quicker by preventing you from allying with them (so you cannot lose more than 4 ships a turn). Additionally, when you win your first offensive encounter, you are allowed to take another turn. You do not have the same luxury when losing encounters, so even the 7-5 ratio is a little bit misleading.

Once you have lost a planet in your color home system, all other colors can choose to attack your 0 defense planet in your home system. This means that it is even harder to lose ships on the defense, since any player that hasn't established a foreign colony on your home system can just attack your defenseless planet (the other ships are just bystanders), and not make you lose any more ships. When they do have to attack your home system with ships on it, they can always aim the Hyperspace Gate at the planet with the fewest ships on it.

As for when to hurt yourself, you might consider all the possible Flares, Cosmic Cards, and situations that would benefit/hinder your progress at losing all your ships.

Beneficial


Amoeba Flare: Its ability to allow you to lose up to 8 ships in a turn is useful.
Masochist Flare: Once you have your flare, you put a clock on your opponents.
Clone Flare: returning Plague would be useful.
Kamikaze Flare: Free sacrifice
Loser Flare: Auto losses each turn.
Machine: Two turns, although admittedly, this would be just as good if not better trying to get 5 foreign colonies.
Filch (Classic) Flare: cheat legally, returning whatever card you want from the discard/retrieve from the deck/etc. once per turn, or "lose a ship." I think I like those choices.
Negotiate Cards: These will ensure a loss, or at a minimum a loss of 3 ships if you cannot "come to a deal." Good thing these cards make up 15 of the 82 cards
Warrior Flare: Useful for extra attacks to lose ships after defense.


Harmful


Healer: Healer so definitively makes Masochist a non-power, since it can heal ships removed from the game.
Mobius Tubes: A complete setback.
Reincarnator and/or Flare: Can make you switch powers, whenever you lose.
Sorcerer Flare: Negate your power


You can only be certain of half of the Flares are in the deck, based upon the Aliens your opponents are playing as. The remaining 5 Flares are random. All in all, it is much more likely that your opponents will draw a Mobius Tubes, and you won't have a Card Zap to counter, than you will have a good selection of beneficial flares in the deck that you actually draw. Masochist is one of the weaker powers, and since you are allowed to choose between two different aliens at the start of the game, it might be best to consider which alien race is worse than Masochist.