Hi,
Your 24" width is probably too small to print most flags but if want to give it a shot you need a smaller rotary calendar/heat press. Expect to pay around $10-12K for a decent entry level press unless you want to import one or find a used one.
If you purchase one with an electric heater (versus oil heater) they don't take too long to warm up or cool down. You have a smaller printer so you really shouldn't be looking for anything other than an entry level press unless you want really get into this big in the future. Either way, I think a smaller press is what you want. You do need to make sure the press does a specific cool down cycle which is what the other person who responded is cautioning about but imho it's not that big of a deal and easy to do.
We have a digiheat 44" which is outdated but they have good support and is a very solid easy to use press. It's the 44" on this page and I think it runs $12-14k but there are a lot floating around used.
http://www.digifab.com/equipment/heatpress.htm
There are a ton of other 44" presses out there too. Just make sure that they have an electric heater and NOT an oil heater. Here's one I found after a quick search
https://www.itsupplies.com/product-p/f-236-ttx-44.htm
The speed of the press is directly related to the heating drum size. I think the digiheat is around 9" diameter or something. The larger the drum the faster you print. Some of the really cheap presses have 6" diameter drums which will be really slow feeding fabric through. I can't personally imagine using a 6" drum model to print flags but I know other people that do it. Even the digiheat feels super slow when you're using it. Larger presses will have 14-18" drums sometimes.
Keep in mind that printing a feather flag or something on the 628 is going to take forever so it's likely not worth it... just something to think about. I had a 628 for a while (trying to sell it if anyone is interested) and I can't imagine trying to print flag transfers on it.
good luck