You can get 15.625ms using app_timer with prescaler 0 and timout_ticks 512. As stated in the documentation, the maximum positive jitter is 3 ticks (91.6us) if multiple activities time out at the same time. You may be delayed by other interrupts as the priority of app_timer interrupt/callbacks is set to APP_IRQ_PRIORITY_LOW.
If you are to use the RTC directly, you cannot use app_timer (assuming you are using nRF51) since there are only two RTC instances with one being occupied by the SoftDevice. Some modules in the SDK (ble_conn_params, app_button, bsp) uses app_timer, so these can then not be used.
