Am I still able to attend my reclassification school if I am Flagged?

Maybe. If a flag is in effect, then no. However, you mentioned the school date is 11 months away, so the key words are "in effect".

When your Article-15 (ART15) was initiated, an 'adverse action' flag was placed on your record. The flag will last until the ART15 is completed and you are given your punishment.

When you receive the punishment, your 'adverse action' flag will be removed and a 'punishment phase' will be placed if the punishment is a month or longer (there are situations where the 'adverse action' flag would be left in place though). This flag will be in place for the duration of the punishment, including any suspended punishment (i.e., you were docked a half-months pay, but it was suspended for six months, the flag would stay in place for six months).

Bottom line for a flag - while you are in an "unfavorable" status, you will have an active flag. When your unfavorable status is complete (all punishment is completed, residuals (if any) from your actions are completed, etc.) and you are once again in a "favorable" status, there shouldn't be a flag on your records.

If I were to gaze into my crystal ball, then if everything about your situation is a simple "you screwed up and got an ART15 slap-on-the-wrist" for it, then the flag should be lifted by the time your school comes around and you'll be able to attend the school .. ASSUMING you aren't deleted from the seat by your unit (the removal isn't automatic if you are flagged - you just can't actually attend while a flag is active).

No. All Favorable Actions (minus Leave) cease to be actioned once Flagged until such time the Flag is lifted. And, when you receive a Non-Transferrable Flag, you are not going anywhere until that Flag is lifted.

Only if the flag is lifted by then...