I use Sly Fibre Max myself and do not experience any issues with IPTV, & i use a Firestick as a 2nd device.
I assume you are Setup Wireless on the device. Is this a 2nd Gen Stick, "As in Latest Alexa" or older?
What speed are you getting via Wireless on the FS?
And, most important... Install STUBEMU on the Firestick, Much better experience & TEST.
Have you also Tested on another device. PC, Laptop etc, do you get the same issues?
Have you Tested with Another Supplier?
You also mention you have only just moved to Sly from BT.
When you first move onto new BB or Fibre, they do a Test for a week or 2 to get your Average Speed worked out on your line, so this could possibly be causing this too