I wonder whether your question is refering to Act III scene 1, which is where Viola and Feste feature by themselves. Ostensibly, all they do is engage in a series of puns much to the amusement of them both, and they verbally spar through their verbal dexterity. This then of course leads Viola to ponder the nature of being a fool, which gives rise to the following paradoxical soliloquy which states that to play the fool actually involves a great deal of intelligence and skill:
This fellow is wise enough to play the fool;
And to do that well craves a kind of wit:
He must observe their mood on whom he jests,
The quality of persons, and the time,
And, like the haggard, cheque at every feather
That comes before his eye. This is a practise
As full of labour as a wise man's art
For folly that he wisely shows is fit;
But wise men, folly-fall'n, quite taint their wit.
The camaraderie that is displayed by these two characters in this scene is perhaps based on their shared love of puns and verbal dexterity. Both, after all, are used to dealing in, if not exactly lies, mistruths. As well, both characters seem to perform a similar function in the play, as they both journey between the two households of Viola and Orsino. Lastly, Shakspeare uses them both at various stages to comment upon the action of what is going on in the play. Therefore perhaps the way in which they interact well can be explained by their similar role and function in the play.