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Indeed you can choose Diploma in Pharmacy (D.Pharm) after B.Sc in Chemistry. In fact, having a background in chemistry is an added advantage since most of the subjects offered in D.Pharm are in the field of chemistry. Here's what you need to know:

Who can get admission in the D.Pharm programme are explained below:
Educational Qualification:

The common minimum educational qualification is 12th pass (or equivalent) with Science subjects including Physics, Chemistry and Biology/Mathematics.
Since you have completed your B.Sc in Chemistry you qualify and even offer more than the minimum qualifications required.
Age Criteria:

Generally, a minimum of school-leaving age plus one year, and in most cases, the minimum age should be seventeen years at the time of admission. For most cases, there is no upper age limit for independent legal surface in the given society.
Entrance Exams:

While some of the states or institutes may demand you to take an entrance test for getting into D.Pharm programs.
What is new with D.Pharm after B.Sc Chemistry?
Stronger Foundation: These points of Pharmaceutical education include pharmaceutical chemistry, Pharmacognosy and other related topics, your B.Sc in Chemistry will assist you in comprehending these areas.
Career Flexibility: After accomplishing D.Pharm you can:
The second step should be the registration of the pharmacist.
Employment in retail and hospital pharmacies.
Hence enter the pharma sales marketing or production.
Shorter Duration: D.Pharm programme normally takes a duration of 2 years and so it is relatively cheaper and shorter than other methods of entering this line of profession.
Other Possibilities to Ponder
If you're interested in advancing further in the pharmaceutical or healthcare field, you might also consider:

B.Pharm (Bachelor of Pharmacy): A 4 year programme detailing more extensive information than the undergraduate level.
M.Sc in Pharmaceutical Chemistry: Closely related to the chemistry degree and allows you to pursue a career in research.
Pharm.D (Doctor of Pharmacy): This programme takes 6 years and emphasizes on clinical practice of pharmacy.