The fastest way to get this item on Battle.net is via trading, you can use the Item Price Checker to see how much Arcanna's Flesh is worth.
Farming it by killing monsters is possible, check the drop rate table below for more information.
It can also be gambled but the chances are very slim.
Arcanna's Flesh drop rate table
The monster with the highest drop chance of dropping Arcanna's Flesh is The Cow King on Nightmare difficulty in The Secret Cow Level of Act 1. Farming the monsters listed below gives you the highest chance of finding that item.
Arcanna's Flesh variants
Below is a list with different variants of Arcanna's Flesh. See the stats of its normal or upgraded variant.