I have this problem in my 2001 Honda Civic as well. I have 167,587 miles on the car and it has a small shift fare like that. tried Lucas, seafoam cleaner and nothing worked. drained and refilled a few times and nothing. so what iv done to fix the problem....if I let off the gas ever so slightly just before it shifts into 3rd gear...it doesn't flare. other then the flare...my car shifts like butter. very smooth and doesn't lack power.

the most likely fix for this is buy the sonnax solenoid adjustment tool, it is a pentagon shaped bit to adjust the dual solenoid at the top pf the trans by the loop you use to pull out the trans, very top. adjust B valve maybe 1/4 turn counterclockwise at a time. could bewrong and it's clockwise but I heard flaring is 3/4 turn counterclock on the B valve. try 3/4 turn and keep tinkering

My 99 does the exact same thing.

On a Chevy transmission I read that the servo can fix this problem I don't know if these Hondas have that

i had this happen to my trans, I ended up replacing the solenoids and it fixed it. i'm sure everyone will have a different case but heres the back story on mine. i replaced my trans at 320k miles and for the new trans, i bought cheap knock off chinese solenoids. it started flaring up on the first drive. i let it ride for a couple weeks and grew frustrated. so i did some research and found another guy having same issue. saw how he bought new solenoids to solve it so i went the same route and voila.

Torque converter