How can I programmatically get the amount of memory currently available from C/C++ code?

The message you have shown indicates a failure to allocate memory for a kernel allocation, not a userspace allocation. It is a request for a 4MB (this is what order = 10 means) block of contiguous physical memory. This is a very large kmalloc() request, and it is not surprising that it fails (likely due to memory fragmentation rather than free memory).

You can find out how much free memory is available in /proc/meminfo, however a more detailed summary is available from the kernel log immediately after the backtrace - starting with the line "Mem-info".

Your backtrace shows that there is 16548kB of memory available, but the largest block is 2048kB (order = 9). So memory fragmentation is indeed your problem.

From reading the source to the tsif driver you appear to be using, it seems that the driver requests a kernel allocation with a size entirely controlled by userspace, invoked by the TSIF_REQ_RX_BUF ioctl() (this is a really bad design, especially given that it doesn't even try to report failures to userspace!). My suggestion is to reduce the size of the buffer you are requesting with this ioctl.