Q:

Why did the Solamnic Knights choose a rose as their symbol?

Any other military order who chose a flower to represent their highest ranking members would be laughed at - so why did they do so?

A:

The rose has a lot of symbolic meaning throughout history.

Love
Honor
Faith
Beauty
Balance
Passion
Wisdom
Intrigue
Devotion
Sensuality
Timelessness

Knights of the Rose, being the highest order, could easily want to embody a number of these symbols, such as Honor, Balance, Wisdom, Devotion, and Timelessness.

The Order of the Rose has always been the most prestigious branch of the Knights of Solamnia. The Rose Knights provide leaders, lawgivers, and exemplars to the Solamnic Knights and the world, guiding others on the path of honor by word and deed alike.
The Measure of the Rose focuses on Wisdom and Justice. DragonLance Nexus

Not sure what it is from originally, but the alternate DragonLance Nexus has this to say

Legends hold that, at the end of his Quest of Honor, Vinas Solamnus knelt in the Whitestone Glade, on Sancrist, and received the investiture by the three gods of the Knighthood, Paladine, Kiri-Jolith and Habbakhuk. When he raised, he saw a beautiful rose of gold blowing in the spot he had been kneeling. He so decided to name the highest Order of the knighthood in this way, to remind Solamnia of this sign of divine favour: and so Paladine took the golden rose, and gave it to King Vinas, who embossed it on his ancient plate armour, over his heart. From then on, the Grand Plate of the Rose has been the armour rightfully owned by the High Justice of the Order; sadly, in the days following the Cataclysm, it was lost.

