Let's take the example of a Sorcerer 2/Cleric 1. The Sorcerer/Cleric can "burn" his or her spell slots in order to obtain a single 5th level spell slot using Flexible Casting. Would RAW only allow them to prepare 1st level Cleric spells, or would it allow them to prepare Cleric spells of up to 5th level because the 5th level slot is not from the Sorcerer's "Spellcasting" feature?
No; they can't prepare 5th-level cleric spells.
There are several reasons this doesn't work. First, a sorcerer needs seven sorcery points to create a 5th-level spell slot, but:
You can never have more sorcery points than shown on the table for your level.
(PHB, p. 101).
A second-level sorcerer thus has a maximum of two sorcery points, and could only create a 1st-level spell slot with Flexible Casting.
Even if the character were a 7th level sorcerer and could use Flexible Casting to create a 5th level spell slot, this still wouldn't work. As the multiclassing rules clearly state:
Spells Known and Prepared. You determine what spells you know and can prepare for each class individually, as if you were a single-classed member of that class.
A 1st-level cleric, no matter what spell slots they have access to for casting spells, can only prepare the same spells as a single-class 1st-level cleric.
The rule for multiclass spell preparation isn't that you can't use slots from your other class's Spellcasting feature; it's that you only consider the preparing class's level, regardless of any other spellcasting abilities you have available.
Finally, even if that didn't apply, per the PHB errata:
Flexible Casting (p. 101). The created spell slots vanish at the end of a long rest.
This is relevant because cleric spell preparation takes place after (not during) a long rest:
You can change your list of prepared spells when you finish a long rest. Preparing a new list of cleric spells requires time spent in prayer and meditation: at least 1 minute per spell level for each spell on your list.
(PHB, p. 58, emphasis mine).
So even if a slot created by Flexible Casting does affect spell preparation, it would vanish (at the end of the long rest) before cleric spell preparation (after the long rest) begins.