https://www.amazon.co.uk/SanDisk-microSD-Memory-All-New-tablets/dp/B013TMNUCA
This card states it is compatible with the new 5th Generation Amazon Fire 7. It is a SDHC card. I assume that this means all SDHC cards are compatible.
I found this information regarding compatibility between the different standards (https://www.quora.com/What-is-difference-between-micro-SD-and-micro-SDHC-and-micro-SDXC-cards):
"This would now mean that micro SD cards are compatible with SD, SDHC and SDXC host products. For micro SDHC cards, they are not compatible with SD host products but are compatible with SDXC and SDHC products. Lastly, micro SDXC cards are exclusively compatible with SDXC host products. "
BTW I took a look at the wikipedia article and that information is not current. It is missing the 7 inch model from the list. http://www.lovemyfire.com/kindle-fire-tablet.html.
Many thanks for your help on this matter.