Hi Marc,
That flexible vent material is made in two versions: single wall and double wall Type B gas vent.
The single wall flexible vent is like the single wall vent - it requires 6 inches clearance to combustible material and to insulation, and it is not allowed in the same locations which single wall is not allowed.
Likewise, the double wall flexible Type B gas vent requires 1 inch clearance to combustible material, however, unlike rigid Type B gas vent, the flexible type is not (to my knowledge) allowed to run through walls, ceilings, concealed spaces and the like as this is not actual "vent" but is a "vent connector".
You are correct, if the flexible material is run horizontally (sloped 1/4" per foot minimum) then it usually also has negative slope sections, which is not allowed.
Also note that the tape used is not allowed to be used.
Plus, the water heater vent looks flattened out facing the viewer.
Is the larger flexible (vent?)(duct?) an appliance vent or a dryer duct?
Here is an example of a double wall flexible vent *connector* installation instructions:
http://www.hartandcooley.com/vent/instr ... ctions.pdfHere is an example of single wall flexible vent *connector* installation instructions (note that this has a 1 inch clearance to combustible material):
http://www.americanmetalproducts.com/ve ... l/flex.pdf