Emirates sells tickets to Krabi using Thai Airways Bangkok to Krabi, so you should have no problem having your baggage "Through-Checked" to Karbi, also if all fights on one ticket You should have the Emirate baggage allowance on the Thai Airways flight.
If your baggage is not through cheeked to Krabi you will have to collect it and recheck it in at Bangkok, the queuing for the main immigration at Bangkok can take over an hour, hopefully the transfer immigration is a lot quicker.
There is very limited duty free shopping when you arrive at Suvarnabhumi Airport, basically a kiosk that sells smokes and booze. You don't have access to the large number of duty free shops on the departure side, you may not see it as I think it is just before the main immigration.
http://www.suvarnabhumiairport.com/e...-boarding-pass
At Bangkok follow signs "transfer to Chiang Mai, Chiang Rai, Phuket, Krabi, Samui, Hat Yai" (immigration, customs and another security frisk).
I presume at Krabi there will be another customs check of bags from international fights not cheeked in Bangkok.