Can I use the per-KM method to calculate motor vehicle deductions for both rental property expenses and self-employment expenses?

No there is not a simplified method for actual business investment expenses. You must use the mileage proration based on business over actual KMs driven in a year against the total of all expenses incurred in a year.

You can use a simplified mileage log book after your full year in business. But this again is used to calculate the allowable expense proration based on the total of all expenses incurred in a year.

This from CRA;

Simplified logbook

You can choose to maintain a full logbook for one complete year to establish a base year's business use of a vehicle.

After one complete year of keeping a logbook to establish the base year, you can use a three-month sample logbook to foresee business use for the entire year, as long as the usage is within the same range (within 10%) of the results of the base year. Businesses will have to show that the use of the vehicle in the base year remains representative of its normal use.

The business use of the vehicle in the subsequent year will be calculated by multiplying the business use as determined in the base year by the ratio of the sample period and base year period. The formula for this calculation is as follows:

(Sample year period % ÷ Base year period %) × Base year annual % = Calculated annual business use

Where the calculated annual business use in a later year goes up or down by more than 10%, the base year is not an appropriate indicator of annual usage in that later year. In such a case, the sample period logbook would only be reliable for the three-month period it had been maintained. For the remainder of the year, the business use of the vehicle would need to be determined based on an actual record of travel or alternative records, as discussed above. In these circumstances, the taxpayer should consider establishing a new base year by maintaining a logbook for a new 12-month period.

https://www.canada.ca/en/revenue-agency/services/tax/businesses/topics/sole-proprietorships-partnerships/business-expenses/motor-vehicle-expenses/motor-vehicle-records.html