I see a few issues you will probably run into, but it can be done!
First, update your calendar as frequently as necessary. The second you get your schedule for the week update the calendar. Also, if you have any semi-regular times that you work, keep your calendar generally marked unavailable for those times (i.e. you're almost always at work around 1 pm, so you wouldn't be able to offer drop-ins or walks between 11 and 3). Also make sure your profile clearly states that you work full time and won't know your exact hours until the week of. Then just communicate with owners! For boarding or house sitting, make sure owners know if you won't be able to come home at all during your shift or if it will be possible for you to let dogs out during your breaks.
Also keep in mind that a lot of owners look for walking or drop-ins during regular business hours, so advertise your unconventional hours as much as possible! This again comes back to your 'semi-regular' schedule, so as much as you can, advertise that because (for example) you often work nights you're a great fit for morning or afternoon walks and drop-ins!
My final recommendation is to try and get as regular of a schedule at your job as you can! Even if it differs by a couple hours each day, knowing you start work at either 9, 10, or 11 am and will be done by 6, 7 or 8 pm is better than constantly changing!