Water – How close can an electric water heater and an electric furnace be to each other

There should be no problem locating two gas burning appliances close together as long as you have proper ventilation. The reason your manual says not to put two items is a closet is that they may create excessive heat when used together. As long as you have good spacing, good venting and a source of combustion air, you will be fine.

While looking at the cap, it's probably worthwhile taking a look at the caulking between the crown and your flue, and or flue-cap, which may have eroded. This needs to be looked at about every year or two (more or less frequently depending on your local habitat, but both extremes in hot and cold weather will help age caulk, rot brick, etc.)