Is it too late to start marching band (for trombone/flute) in 11th grade?

You need to address your question to the director of the Marching Band. Trumpet might be a better choice, as you will have more opportunities to play in bands outside of school.

You would have one heck of a time learning a new instrument to the standard of an 11th grader, evem if you are a fast learner, unless your school has a poor band program. In that case, you could have a chance. I would talk to your director and see what they say. If I were your director, I'd probably say no unless I needed more bodies on the field for marching. Logistically speaking, I'd play flute because if you don't know the notes on trombone, it's visually obvious.

Marching band is only for part of the school year. Although you may be able to learn an instrument to a level good enough for a HS marching band, after marching season it will be concert band time. If you were going to do it, I would go with the flute, trumpet or clarinet. I did what you are talking about but before Freshman year. I started clarinet at the beginning of the summer before HS and was in the marching band in September. I worked hard over the summer with private lessons until December. I became good enough that I wasn't last chair during concert season. I had 5 years of violin before this and was in the top level of the HS orchestra. You cannot get an instrument that cheap and expect it to be any good. Plan on spending closer to $500 for a trombone, $250 or more for the smaller instruments. Be careful buying any used instrument that you don't already play. Woodwind instruments can have bad pads that make it hard or impossible to play and the cost to repair could be another $150. Brass instruments can have issues with the pistons making them impossible to repair. Many of the internet instruments or places like Sams club sell chinese no name instruments, that means no replacement parts. If something like a flute key breaks, you may have to buy a new instrument. The slide on a trombone is extremely important and must be very smooth in its movement.

Marching band is really fun, but it's going to be hard to learn flute/ trombone in 1 year. The marching music isn't easy, and your school directors might not allow a beginner in the band. Also, there really aren't any $100 instruments, but you can check one out from the band with little or no charge. Though I play flute, brass instruments are easier to play than woodwinds, so I'd go with trombone.