Fire does not directly ignite or spread to burn flammable objects.  The attached image shows an attempt to burn leaves, vines, oak planks, scaffolding, a peeled oak log, a bamboo tree, and an oak sign with flames applied directly to objects or placed on adjacent blocks.  I ran this test for 15 minutes IRL, and there was no effect to any of the objects.

After reviewing the bug database, I note that this issue has been patched for the Java edition, but I found no mention of a patch for the Bedrock Edition.

Note: I was forced to enter this bug as impacting the 1.16.0.60 Beta, but my system has not yet loaded that software, so I am still using the 1.16.0.59 version.