The first thing is to note that vibrant, brightly-colored objects are by nature more attention-getting, so I hope your bike is not bright red, light orange, yellow or bright green. I have noted that gray bikes are less noticeable and even hard to see in some conditions. Dark blue, dark gray, pale or dusty white, and brown are also favorable colors to make a bike less noticeable.
I have seen many bikers disguising their machines by wrapping the frame, or parts of it using duct tape. Some types of duct tape are less shiny than others, and some have a rather weak adhesive that won't be too hard to remove. The advantage of duct tape is that being skillful, you don't need to take apart the bike.
With bikes that have straight tubes, you can find some PVC leftover piping that you can cut lengthwise in order to make a sleeve to be inserted around tubes. Depending on the pipe fitting it can even look very cool, but the point is, PVC is very easy to paint with spray paint or many other types, so you can "uglyfy" the pipe as much as you want, but you can remove it from your bike if you want. Having more patience you can make covers for the joints in the frame and make the PVC piping fit really well so it won't be obvious that it has a cover.
As for the components, you can cover then with a lot of materials, for example I use a sleeve made out of old inner tubes to wrap the crank arms, held in place with zip ties. I made that for protection actually, but it cleverly covers also the brand name tag. This very same technique can be used in chain stays, seat tube, handlebars hubs and even brake or shifter levers. Just make sure that the tube isn't "too black" nor shiny. This material can be almost invisible in twilight conditions and cluttered environments, so almost any other bike will drag more attention than yours.
For other components, like derailleurs, shifters, levers, I would recommend to partially cover them with "hot glue" and let the glue become dirty. The hot glue won't stick too hard on metal, so it will be easily removable. There are transparent and non transparent types, I recommend the latter as it disguises branding better. Use it wisely to cover badges and the like, but don't make it get into pivots or anything. You can stain the glue with black oil, grease or dirt making it look even uglier. You can add dirt and dust when the glue is still warm.
I give this advise based on experience and what I've seen other riders do in my city. I use some of these tricks, not all of them. I personally commute on a dark blue bike that is not so shiny, and most my components are matte black or matte gray and generic (so I don't have brand badges to cover). I have left the bike unlocked among a lot of motorcycles at my workplace and nothing has happened to it without making it look like trash ;) but I can assure you that this bike is hard to see, to the point that to myself, when I'm approaching the parking lot it's hard for me to find it from a distance, even knowing where it is!
Finally a note of advice on safety: Disguising your bike and making it less noticeable is dangerous in traffic, so make sure you use bright of reflecting clothes, reflective straps on ankles, elbows, wrists, etc, a bright helmet, a bright backpack or whatever you find useful, so you are easily seen by drivers and pedestrians! You can attach the blinking lights to your backpack instead of the bike, as long as they are correctly positioned and oriented, they will serve their purpose.
Good luck with your project!