what effect is this

There are several ways to accomplish this. 

First I see splatter brushes where used to give to create the paint or coffee stain marks.  Easy.  You can find a million for free.

To fit things into a shape that is also easy.  You can create any shape in Illustrator and then place an image into.

But honestly.... I think this was probably done in Photoshop.  First the flag was a painting of a flag that was distorted or simply painted that way.  It is also easy to cut an image from a shape in layers that have not been flattened.  Then like I said... using the splatter brushes that look like spray paint or coffee stains give it that grunge effect.  This all can be done in Illustrator too.  But I would bet money that this was done in Photoshop.

Could be any crazy effect probably in PS not in Illustrator. You can achieve something like this effect using Opacity Mask. But I will go with effects in PS.

Chana

Try Photoshop.

Agreed. Effects of that type are raster-edit territory, and there's really no good reason to pursue it in Illustrator.

It has probably not been done in Illustrator at all.

I guess you have a clean image of a flag and want to make it look like that? Try Photoshop.

It looks like a raster opacity mask. An opacity mask in Illustrator can hold both vector and raster.

Select the mask (on top) and the image (below). You select on the artboard or target in the layers.

Click on "Make Mask" from the Transparency panel

The right side shows the opacity mask once set in the Layers panel and the Transparency panel.

Hope this helps.

You will need to apply a custom texture via the opacity mask.

https://m.youtube.com/watch?v=PtFV8X8cONQ

https://m.youtube.com/watch?v=ks4Q3m4JcCU

and here:

Creating and Using Textures for Design