I have had a lot of success with gluing PLA and ABS parts together with Simple glues like Super Glue and the glue you get in model kits like Airfix but have not tried with flexible filaments. The flex filaments I have are PLA based and cannot see why they would not glue together.
Another technique i use for fixing parts together is welding with a 3D pen. You can get a 3D pen for as little as £15 from eBay and Amazon. This would enable you to use the same filament and physically weld the seems together just like welding metal. The join is incredibly strong and would work with every kind of filament that you printed the parts from. I have then successfully sanded down the welds (PLA / ABS) with a dremal, hand file and sandpaper.
The welding with a 3D pen technique is also very handy for adding small details or even fixing breaks / cracks / holes. Or even just to thicken an area for added strength.
Flexible parts are cannot be glued, as others have recommended they must be welded. Best tools for this are a soldering iron or a 3d pen, but if you get a 3d pen for this purpose, make sure it can do flexible filaments.
Plastic welding, rubber cement and acrylic adhesives have varying amounts of success. Are you trying to adhere static plains or does it need to bend at the adhesion point?
I have confirmed that Gorilla Glue works, in particular I am using the Gorilla Glue Pen (not the superglue). I am printing a belt out of TPU for my wife’s cosplay that requires me to print it in 7 pieces, following the directions I wet the area to be bonded (both sides) with a damp paper towel, put the glue sparingly on the mating surface and placed the other part on top, I then put some weight on it (a small box with a couple hard drives in it) for an hour, once the initial cure completes the shearing strength feels good, (can’t pull them apart by stretching the belt) now I was able to find a spot that I missed the glue on and was able to peel the parts apart but even that was pretty tough to do.