There needs to be a lower and an upper flashing on all sides of a chimney.
I am going to presume you are talking about a masonry or brick chimney for point of reference. Please correct me if I am wrong.
On the lower section of the chimney, which is the side that faces the gutter or eave edge, there needs to be a Roof-To-Wall Apron Flashing. The bottom portion of the sheet metal covers the top portion of the row that butts up to the lower bottom side of the chimney. The top portion of the sheet metal Apron Flashing then goes up vertically on the face of that lower side of the chimney. It needs to be Wider than the chimney and fold "Ears" or "Tabs" of sheet metal around the corner of the structure.
Then, both the left and right side would have "Step Flashings" installed, which are also commonly called "Baby Tin" flashings, which are individual 90* bent flashings, which get weaved in between each successive course, or row, of shingles, as they proceed up the slope of the roof. At thetop corners, they extend past also, so that they can fold around the corner.
Then, on the Top side of the chimney, the side which faces the Peak or Ridge of the Roof, get a flashing called veral names, ie; Pan Flashing, Apron Flashing, Saddle Flashing, (If a saddle or cricket is required, but that story is for another day).
Then, all 4 sides of the chimney need a second piece of sheet metal installed, which is called the Counter-Flashing. Most traditionally, the Counter-Flashing gets installed into a sawed out mortar joint, called a Raggle or Reglette Joint. This can be installed in a Step-Fashion, or as a perpindicular joint to the slope of the roof. Also, some choose for preferance to not cut into the masonry structure and Surface Mount the Counter-Flashing. The Counter flashing then needs to be secured to the structure with masonry anchors of one type or another.
So, in answer to your question, Yes, a bottom flashing is necessary for a proper flashing job to remain water-tight.
Could you please upload some photos of the chimney you are referring to, so that a proper view could be made of it and advise given more accordingly to your exact situation.
One more thing.....If the chimney rests on the Ridge of a roof, where part is on one slope and part is on the opposing slope, then the amount of sections would require 6 sections of sheet metal and then the appropriate counter-flashings to be installed.
Ed