- As of yet Unknown.
Flower Power may have the ability to prevent or stall a conflict.Erf-b1-p013 It may also directly affect plant life. When we first see Sizemore and Janis, they are sitting next to a giant flower. Might Janis have grown that flower to its huge size during Sizemore's lesson? If Flower Power allows casters to quickly grow giant plants, then they could prevent conflicts by growing barriers of giant plants between conflicting sides.
Flower Power may also have limited control over plant life.
1) To speculate on Flower Power, let's note that there are few references at this time, but we may infer certain aspects from its sister Classes and Disciplines and the evidence we have. Flower Power is the confluence of Life, Matter, and Erf, Classes and Axis respectively, which places it in the Discipline of Hippiemancy. (It may be worth noting, Flower Power might also be defined by the absence of Motion from its Classes.) The use of magic in other Disciplines of Erf are well known to Erfworld fans, such as Dirtamancy, Lookamancy, and on at least two explosive occasions, Shockmancy. The Erf Axis schools for their Disciplines appear to be strongly physically based as might be inferred from the Erf Axis. In this way, Flower Power might also be physically grounded in Erf for the Hippiemancy Discipline. As it is related to the confluence of Life and Matter, this may place its effects on physical environment (matter) which is experienced by Erf beings (life) (like Gaia in the real word.) For example, Flower Power Flaking appears to impact the experience of time. In the one example we have, this effect was experienced as physical time dilation  in a localized space within a single hex and not by beings outside of that space, however, for you Signamancers out there it would appear Flower Power's sister Discipline in Erf, Turnamancy, may be required to impact turn-based time between hexes or perhaps sides. Based on visual references and the deference of Janis, Grand Abbie, to the plight of others, Flower Power may stress communitarian/egalitarian values which it may share with its fellow Hippiemany Disciplines, Signamancy and Date-a-mancy. Looking for inferences into Flower Power from it's sister Disciplines, Signamancy and Date-a-Mancy does not provide much additional evidence at this time as they too are not locked in much Canon. With their confluence of Life and Matter and their absence of Motion Classes, it may be that within Hippiemancy Flower Power (Erf) might influence the environment/nature (space), Signamancy  (Fate) might influence perspective/insight (vision), and Date-a-mancy  (Numbers) might influence synchronicity (time in meaningful events, or put another way, the inverse of meaningful events in time).
2) Hippiemancy is the magic of relationships: detecting and altering the forces of opposition and attraction which bind people or units. Flower power may relate most to bending and breaking the rules of erfworld using loopholes; and distort perception of time. If Parson is flower power capable and spent an entire night wishing that units could move at night, he might have been able to move only at night from that day onwards (explaining his failure to walk out during the day) yet not realising his newfound abilities.
3) If Flower power has control over plants it may help improve (or possibly destroy) food production.
4) Flower power may also be related to herbalism on stupid world prime.
- JanisErf-b1-p011 -- likely named after Janis Joplin, a singer and artist closely associated with the real-world Hippie movement.
Real World References
"Flower Power" was a slogan used by the 1960's-70's peace movement whose practitioners were known as Hippies. They worked to end the war in Vietnam, fought racial injustice, and attempted to revolutionize the American way of life. Their ideology included non-violent protest and passive interference with authority. Their clothing was usually vibrant, and they were frequently associated with drug use, psychedelic music and art, and social permissiveness. Their personal artwork (rather than the work of the professional artists associated with the cause) often featured simple, colorful floral designs, which appeared on their clothes and vehicles. Flowers were a significant symbol during their peace protests. For instance, hippies would place flowers in the muzzles of guns carried by National Guardsmen (sent to maintain order at various gathering places of the movement) demonstrating their own non-violence and hoping to sway the young men into ignoring any orders to use their weapons. Tragically, it didn't always work: at least two incidents of US National Guardsmen shooting hippies occurred. Flower Power died with the Hippie movement, absorbed or destroyed by other sub-cultural movements, and with the ending of the War in Vietnam disappeared quickly. The participants had matured into adults with responsibilities, their most serious causes had been eliminated, and they had discovered the self-destructive and addictive qualities of their philosophical ideals had taken a toll on their lives and well-being. The Hippie movement remains one of the most respected revolutionary movements for its lack of violence (perhaps exceeded only by Gandhi's success in India, on which the Hippie movement may have been modeled), thanks in part to its success in both the anti-War and racial arenas.