With a fork or in a blender, mash blackberries to a pulp. Strain the pulp through a strainer to remove seeds.
Pour the blackberry pulp into a small pot, add coconut milk, lemon juice, regular sugar and coconut sugar, and agar agar. Whisk to combine, then bring the mixture to a boil, and on medium let simmer for about 2 minutes, stirring occasionally.
When the agar agar has melted, remove from stove, let it cool for a minute or two, then pour the mixture into small durable glasses. Leave on the counter to cool completely. At the beginning of the cooling process you may need to stir the mixture occasionally to fully combine it, or the coconut milk will likely separate. You only need to do this every couple of minutes or so until the liquids start to solidify. After that, don't stir it any more, but just let it rest and cool down.
Once cooled, cover the jars with a lid and transfer to fridge to continue cooling and firming, for at least 2 hours, or ideally, overnight.
When ready to serve, remove the vegan panna cotta from the fridge, remove the lids, decorate with fresh berries or berry sauce and add a sprinkle of toasted coconut flakes.