This sentence wouldn't be a natural choice of words for a UK English speaker. The use of 'spell' to mean 'a few moments', and 'figure out how' are typical of informal American usage. In GB English, we'd be more likely to say 'rest a bit' and 'work out how'. We'd understand from the context that 'for a spell' meant 'for a short while', but we wouldn't use normally use the word in this way. In the UK, we do use 'spell' to mean a period of time, but only in specific collocations, and usually preceded by an adjective. For example, you could say 'He had a short spell working as a swimming coach'. Also, 'a cold spell' is a period of a few days or weeks of cold weather, and 'dizzy spells' are periodic bouts of feeling faint and nauseous.

"To rest a spell" is natural. It is VERY informal and is mostly used by older people and country (rural) people. I would suggest using "rest a while" and "rest a bit" as more common and "natural".