Yes, that too. As a matter of fact, generalists stand to gain a lot from having the combo Study Bonus - Free Study - Book Learner. IIRC, that would allow to increase benefits of studying either source by 1.5.
As for the generalist Flambeau School, I'm quite persuaded that the defining "school" Virtue should really be Major Magical Focus (Damage). It's just a perfect fit for the purpose of the school. (it covers all but the Rego projectile magic). That being a Major Virtue, what to do of the Flambeau "free" minor Virtue ? Personally, I'd allow characters to buy that as the free Virtue, provided a balancing extra Minor Flaw (Hermetic or Supernatural) is picked to pay for it. Something similar to the Ex Miscellanea system. One might justify it by the fact that when a Flambeau enters the school he is initiated into MMF (D), and the typical script has loss of the vanilla Flambeau Virtues (esp. if they are Puissant Forms) as an Ordeal. Alternatively, one might buy the Mutable version of MMF (D), which is a minor virtue.
Other good Virtues to have for this school would be Puissant and/or Affinity in any of Creo, Perdo, Rego, Penetration, and Finesse. And the aforementioned Study Bonus, Free Study, Book Learner. Since this is meant to be a generalist school, the character should not have too limited a focus in any hermetic Art or method of study, so that if one has an Affinity, it should be at least one of a pair, at least. i.e. if one has Study Bonus, it should also have either or both of Free Study or Book Learner. If one has Puissant Creo, it should also have Puissant Perdo or Rego, and/or Puissant Penetration or Finesse, and viceversa. Skilled Parens and Self Confident are also appropriate, too.
To complement the Focus in damage, one could also develop a Potent Magic in Rego projectile magic. I dunno whether it would be minor or major.
Our generalist War Wizard Flambeau could either focus on precise, powerful applications of formulaic magic, in such a case either Flexible Formulaic Magic or Flawless Magic would be appropriate (both if you can get them by Initiation by other members of the school), as well as Life Boost and Method Caster, or on flexible, creative uses of spontaneous magic. In the latter case, either (or both if you can Initiate them) of Diedne Magic, Chthonic Magic, or Life-Linked Spontaneous Magic are very appropriate. Enduring Constitution, Withstand Casting, and Spell Improvisation are also good complementary Virtues to have.
As it takes mystery Virtues, Charm Magic, Spell Timing, Animae Magic, Glamour, Hermetic Theurgy, Names of Power, Invocation Magic, Synthemata Magia, Hermetic Geometry, and Consummate Talisman are all good Virtues for develop, both for the formulaic and the spontaneous War Wizard.
As for Flaws, a broad attitude for destructive magic often indicates a mystical sympathy for aggressiveness, poor impulse control, a bit of anti-social attitude, and a tendency to go "wild" and loose with one's magic, as represented by Flaws like: Careless Sorcerer, Deleterious Circumstances, Magic Addiction, Rigid Magic, Unstructured Caster, Loose Magic, Restriction, Unpredictable Magic, Blatant Gift (or Social Handicap), Fury, Personality traits and Flaws that indicate a problem with impulse control (Ambitious, Proud, Lusty, Wrathful, Optimistic, Carefree, Overconfident, Reckless), Bound Magic, Fettered Magic, Poor Memory, Poor Formulaic Magic, Susceptible to Divine Power, Supernatural Nuisance, Vulnerable Magic, Vulnerable to Folk Traditions, Warped Magic, Weird Magic, Greater or Lesser Malediction, Lycanthrope, Chaotic Magic, and Weak Enchanter.
A basic feature of the Generalist Flambeau school is the acknowledgement that the vast majority of the Flambeau combat techniques is based on one among three Hermetic Techniques: Creo, Perdo, and Rego. Therefore, members of this school strive to maximize all of these Arts. As it concerns Forms, the vast majority of them can have useful combat applications. Elemental Forms (Au, Aq, Ig, Te) have both good destructive potential, widespread presence, and usefulness for either or both of direct damage and projectile attacks. As a result, all generalist war wizards strive to develop all or at least 2-3 of them. In most areas, He may also be a good substitute for elemental Forms, so some generalists study it, especially if they spend much time in wilderness areas. Co is fundamental for employing Perdo spells and some elemental attacks to their full potential, so all generalist Flambeau strive to have good mastery of it. Like He, An may be useful to develop if the mage spend a signficant amount of time in the wilderness. Me and Im have less of direct combat potential, but some generalist war mages come to realize their usefulness for subtle attacks, distractions, and defusing unnecessary confrontations, so they may often develop their abilities in either of these Forms (although not both of them, generally). Typically, Me is the more common choice. Vi is developed to a good degree of mastery by most generalist Flambeau, thanks to its fundamental value in fighting demons, spirits, and all kinds of magical creatures, as well as the combat applications of metamagical spells.
As it concerns Abilities, Concentration, Parma Magica, Penetration, and Finesse are as important as the Arts for the generalist war mage, and they develop them accordingly. Athletics, Awareness, Brawl, Chirurgy, Stealth, Survival, and all Realm Lores, may have some usefulness for combat specialists, so few generalist Flambeau are confortable in remaining completely unskilled in them.
The generalist Flambeau school was born out of two main sources: the first was the mages who in the course of their lifetimes managed to master several other Flambeau schools, then realized the basic common factors (such as the reliance on the combat Techniques) underlying many of them, and strived to transmit their apprentices a unified approach to magical combat. Other mages had aptitudes and peculiarities of one's Gift (such as a focus for damaging spells, or affinities for multiple Arts), that made them sympathetic to a skill of magical combat that downplayed the overreliance to any one Art. Their combat techniques spread among those Flambeau that preferred a generalist approach to Hermetic magic and valued flexibility over specialization, and became popular among those mages who lacked the means to specialize to a very high degree in any one Art, such as mages from Spring Covenants, without very good books or high amounts of Vis in any one Art.