This is theoretically possible but practically the cost would be too high for an average consumer to do this right now. Right now, to learn about an organism's DNA, we'd have to first (1) sequence the DNA (actually read the raw DNA in) and (2) analyze the sequenced DNA. iGenomics is free and so the "DNA tricorder" software is free. However, the most affordable DNA sequencer as of now is the Oxford Nanopore MinION (https://nanoporetech.com/products/minion), which starts at about $1000. Oxford Nanopore is working on a more portable, and hopefully more affordable version, called the SmidgION (https://nanoporetech.com/products/smidgion) that they hope to have out within the next few years.

I'd estimate we are about 3 - 5 years away from hitting the point where ordinary people start to own DNA sequencers.

Worth noting, while DNA could be useful here, there's likely more affordable ways to differentiate between plants today.