If they are an Employee, going from job to job, the deduction for Unreimbursed Employee Expenses ended in 2017 so no mileage claim is possible.
If they are self-employed, the mileage from home to the First job and the Last job to home are not deductible. Nobody gets a deduction for driving to work and home from a single location.
If you are self-employed and your office is located in your home, you can deduct miles you travel to meet with business clients or perform other business-related functions. This is from pub 463:
Office in the home.
If you have an office in your home that qualifies as a principal place of business, you can deduct your daily transportation costs between your home and another work location in the same trade or business. (See Pub. 587, Business Use of Your Home, for information on determining if your home office qualifies as a principal place of business.)