You want to achieve two things: Keep the paste homogenous, in this case keep the flakes from settling, and dose reliably into bottles.
For the first task, you need a mixing bowl or hopper. At a skim, the links provided in Freds answer seem to go in the right direction (but you will need lower speed mixers, since you just want to suspend, not disperge). Since you gave no information on viscosity, amount produced in one batch, other considerations (heating? cooling?), we can't guide you any further for now.
For the second step, you need a dosing pump. A dosing pump is any positive displacement pump that can be controlled in a way that it delivers reliable batches. Typically piston, progressing cavity or peristaltic pumps are used. Again, we can't guide you any further as we lack important information. However, given that you likely have small batches and a small budget my first look would be these two types of pumps:
Peristaltic pumps: Only one part (the tube) touches the medium and get a pretty exact dosing result by controling the no. of revolutions per batch. These are likely to be affordable.
Diaphragm pumps: If you manage to find one that lets you fill one bottle with round number of strokes, you will again have a relible dosing result at a lowish cost. Cleaning could be a bigger hassle.
So you want to look for food grade mixing hopper or mixing bowl with a (food grade!) dosing pump. I don't work in food processing, but my hunch is that the exact application of your friend is boringly common and you can get a mixing hopper with dosing pump as an integrated unit.
Before going on a shopping spree, your friend should educate themselves on the important regulations. Likely they will have to clean and thus dissasemble the device every working day & thousand other considerations.