Evasion doesn't stack
Unless it specifically states otherwise (and some of them do), gaining duplicates of class abilities doesn't do anything special. You just get the ability to do... something you can already do.
For things with effects based on level, like Turn Undead and Wildshape, whether or not they 'stack' with each other to determine what effective level (EL) you use the ability at is complex thing that depends on FAQ answers and the specific sources of the ability and stuff. It's a whole nother answer worth of information.
Evasion does not stack. Uncanny Dodge, another rogue ability, has a specific caveat;
If a character already has uncanny dodge from a second class, the character automatically gains improved uncanny dodge instead, and the levels from the classes that grant uncanny dodge stack to determine the minimum rogue level required to flank the character.
So a common house rule for multiple sources of Evasion is to grant the character Improved Evasion.
If you have class that grants an actual Feat, like Ranger grants the Track feat, and you already have that feat, unless the entry says 'if you already have the feat, you may pick another' or something similar, you just get.. nothing.
A common houserule is that you get to pick a different feat in those circumstances.
Even with that houserule, though, gestalt's basic rule is that if you get something from both sides of the gestalt, it overlaps, it does not stack. This is applied to BAB and saving throws explicitly, but a common houserule applies it to everything - so you can't dual-progress Sneak Attack by playing a Sneak Attack Fighter//Rogue, and you can't dual-progress your Wizard casting by playing a Wizard//Something/Loremaster.
So basically, under the rules, and under the common gestalt houserules, that character gets nothing special for getting evasion twice. Equally though, many tables grant Improved Evasion when you get Evasion twice, so you could go with that.
By RAW, you get nothing. By houserules, you could get nothing, or you could get improved evasion, or the GM might feel nice and grant a feat or a bonus to reflex saves or something. It's up to the GM, though, there is no explicit rules granting you anything at all for getting Evasion twice.
However, there is stuff that trades Evasion away
While you can't get Evasion twice by RAW, you can trade Evasion away once and still receive Evasion, such as by an Alternate Class Feature, or a Level Substitution. I'll list some of the better ones here.
- Spell Reflection [Complete Mage] - Trade evasion for the ability to reflect targeted spells that miss you.
- Dungeon Specialist [PHB II] - Trade evasion for a climb speed.
- Mettle of Mountains (Goliath Rogue Substitution Level) [Races of Stone] - Lose Evasion, gain Mettle (and bonus to Fort saves).
