I get this phone call several times a year, and it is a common problem that is easily fixed (usually.) In a nutshell, what is happening is smoke is being pulled from one flue top across a short distance horizontally and being pulled down another flue into the house through a fireplace opening.
One way to handle the above situation is to stagger the height of the flue tiles.
In the photo above, an additional flue tile has been cemented to the top of the center flue tile, thus staggering the height and eliminating lateral smoke transfer. Flue tiles can be purchased at brickyards. When adding a flue tile, cement it to the existing tile with mortar mix. Then secure it to the tile below it with strips of plumbers tape and masonry screws on at least 2 opposing sides. 3 sides would be even better. At most hardware stores you can purchase the masonry screws (Tapcon screws) individually (as opposed to a 50-count pack) which will save you money. You will need to purchase a masonry drill bit that is one size SMALLER than the diameter of the Tapcon screws. The 1/4″ diameter screw will require a 3/16″ masonry drill bit for drilling the holes. You use a bit that is one size smaller than the screw diameter because you are drilling a pilot hole for the 1/4″ screw to drill through and have a tight fit. Tip: have a spray bottle of water to spray the bit and hole while you are drilling; doing so will increase the life of the drill bit. A 1.25″ screw length is sufficient. Tin snips will be needed to cut the plumbers tape to length. I use a nut driver in my drill to screw in the Tapcon screws. You do not want to install these screws with high speed because you risk snapping the head off of the screw, so adjust your drill speed setting accordingly. If you are using an electric drill that does not have a variable speed adjustment, then back off on the trigger to back off the speed. Cordless drills usually can be adjusted.
In the case of two or more round metal chimneys being too close to one another and level with one another, the solution ends up being the extension of one of the flue pipes to achieve a stagger of heights. This gets a little more complicated, as you have to try to find parts. You may or may not find the chimney pipe you need. You would need to know the name manufacturer of the chimney pipe. You usually cannot mix and match from other manufacturers without voiding the UL listing of the product. If the UL listing is voided due to using non-approved parts, then any warranty of those parts is void. You may want to call a pro at this point.