Can you mix Red Onion chutney into bread?
Yes, you can add the chutney to the bread dough to produce a more flavorful bread.

When you add the chutney depends on exactly how you want it distributed in the bread.  


If you'd like the chutney flavor to permeate the bread throughout, mix directly in with the wet ingredients during the initial mix.
If you prefer to have "streaks" of chutney or layers, you can proof the dough first, and just fold it in a few times before the final rise and bake.


Depending on the texture of the chutney and how much you add, these different approaches can have different effects on the finished product.  For example, if you're adding just a small amount of chutney and it is already pureed or mashed, mixing it early could dilute it in the dough so much that it won't give much flavor to the bread.  In that case, waiting to add it later and folding it in could produce "streaks" of flavor that might be a nice effect in the final bread.

If, on the other hand, your chutney is rather "chunky" or you're adding a large quantity, it might be better to mix it in earlier.  Adding a lot of big chunks after proofing can produce layers in the final bread that can separate, make baking more difficult (with pockets of "filling" that don't rise in temperature as fast), and/or make the bread difficult to slice.