Q. Is there any issue with placing flowers on Jewish graves?
There are certainly ancient precedents for flowers or spices on dead bodies, but this was probably for the sake of a pleasant smell. Talmudic sources record the placing of myrtle twigs on bodies; halachic works even permit the myrtles to be cut on the second day of a festival. However, because idolaters often placed flowers or incense on a grave, Jews deemed this to be chukkat ha-goy, a gentile practice, and discouraged its emulation amongst Jewish communities.
The Jewish usage came to be simplicity and equality in all aspects of a funeral, especially in the choice of shrouds (before the current usage developed, shrouds were often made of dyed material and in the case of wealthy people they were sometimes very elaborate). Theological principles were applied to the non-use of flowers, e.g. Isaiah 40:7-8 was quoted: “The grass withers, the flower fades, but the word of God is eternal”.
At Masonic funerals there is a custom to throw a sprig of acacia onto the coffin as a token of resurrection. Jewish Freemasons follow this custom without comment though it may have emerged from Christian thinking. The Jewish condonation of the practice is probably for public relations reasons, though if a rabbinic authority were asked the answer would be likely to be negative. A negative attitude would probably also be adopted in relation to planting flowers or shrubs on graves because it is forbidden to derive any benefit from the earth of a grave.
Coming back to flowers on graves, there is an additional practical problem in that in places where floral tributes are placed on graves it is unpleasant to visit the cemetery after a few days and see dried-up or smelly remains of flowers which no-one has cleared away. If one wants to spend money to honour the deceased, rather than paying for flowers it seems better to support a cause that works for the welfare of the living.
Those who want to show that they have been to the grave would be well advised to follow the common Jewish practice to place a stone on a grave as a mark of respect and to show that the deceased has been remembered, even though this custom possibly arose in ancient times when graves were topped with cairns and there was a danger of the stones being scattered by vandals or the wind.