'Big Time Rush' Star -- American Airlines Smashed My Custom Guitar

"Big Time Rush" lead singer Kendall Schmidt is having issues with the airlines again after his custom made guitar was destroyed in flight ... and he demands American Airlines pony up.

Kendall had an appearance in Sacramento Sunday where he was supposed to perform ... but showed up with a mangled piece of wood instead of the $4,000 guitar he bought 6 months ago.

And Kendall says American isn't making things easy ... informing him he shouldn't expect any answers for at least a month.

American has a liability limitation of $3,400 for domestic flights ... so, best case scenario, he'd be out $600 ... unless he got insurance.

Kendall's had other airline woes ... he says a bag with $7,000 in jewelry went missing last year.

We've reached out to American ... but they must have lost our number.