The tube is getting "weak" as was stated earlier. You can have a repai shop try and Restore or "rejuvinate" it, but it's a 50/50 type deal an may fix it up for a few weeks, a year, or kill it completely. I've don a few with decent results, but like I said it's anyones guess to how i would work out and for how long.
If it just started doing it you can turn the Screen voltage up a tad o the flyback and get it to settle down a little, but you end up with brighter washed out picture and are only prolonging the blinking again You can also defaet the IK circuit that monitors the tube current, tha would have to be done at a repair shop for sure, unless you're hand with the soldering iron and know your way around the inside of a TV Then you end up having a color that's slightly off because there's gun going bad and causing the current the IC monitors to be off, so i blanks the screen, it settles down and starts all over. Once it warm up, like you said, it will be OK (usually), but that will take longe and longer as time goes on until it either doesn't come on or blink all the time.
See if any local places can do a tube restore on it and what it costs If it just started acting up you may be able to squeeze a little mor life out of it, but it's dying and there's not much can be done t correct it but relpace the tube. That would cost what 2 or 3 new TV' of the same size would